This paper is about ‘Winograd Schemas’, to be described, and how they may be interpreted by means of the ‘SP System’, to be described.
In a ‘background’ section, next: there is first a description of the concept of a Winograd Schema; then the SP System is introduced, with a link to Appendix A where a fuller description may be found; lastly, there is a selective review of related research, with remarks about the significance of Winograd Schemas in AI and, more specifically, in the study of ‘commonsense reasoning’ and ‘commonsense knowledge’.
The main body of the paper (Section 3) presents three Winograd Schemas, each with a demonstration of how it may be interpreted by means of the SP System.
2.1 The concept of a Winograd Schema
In a paper published in 1972 , Terry Winograd gave an example of a pair of sentences:
The city councilmen refused the demonstrators a permit because they feared violence and
The city councilmen refused the demonstrators a permit because they advocated revolution
which are easy for people to understand but are problematic for most AI systems—because the meaning of the word “they” in each sentence depends on a “sophisticated knowledge of councilmen, demonstrators, and politics” (p. 33).
Since then, researchers have gathered together many such pairings which, in a similar way, differ in only one or two words, that contain an ambiguity that is resolved differently in the two cases, and that requires the use of world knowledge and reasoning for its resolution. Some of those pairings—instances of the afore-mentioned “Winograd Schema”—may be seen on bit.ly/2MPm64B.
For the sake of brevity in this paper, ‘Winograd Schema’ is shortened to ‘WS’ and ‘Winograd Schema Challenge’ is shortened to ‘WSC’. Since each item in a WS pairing may comprise two or more sentences, it is wrong to refer to them as WS sentences. Instead, they will be called ‘WS items’ or ‘WSIs’.
Important features of any WSI include:
“It should be easily disambiguated by the human reader. Ideally, this should be so easy that the reader does not even notice that there is an ambiguity …” [6, p. 557].
It should not be possible to interpret a candidate WSI correctly using “cheap tricks” aka5, Section 2.2]. For example, with a question like Could a crocodile run a steeplechase?, we can say “no” because we have never heard of such a thing, without bothering to consider the physical demands of a steeplechase, the short legs and aquatic habits of crocodiles, and so on.
In a similar way, with a pair of sentences like these: The women stopped taking the pills because they were [pregnant/carcinogenic], the meaning of “they” is obvious in each case because only women can be pregnant, and only pills would be carcinogenic [4, Section ‘Pitfall 1’].
The test should be Google-proof. With respect to the previous example, Levesque says “In linguistics terminology, the anaphoric reference can be resolved using selectional restrictions alone. Because selectional restrictions like this might be learned by sampling a large enough corpus (that is, by confirming that the word “pregnant” occurs much more often close to “women” than close to “pills”), we should avoid this sort of question.” (ibid.).
There should not be too much ambiguity about the answers, as, for example, in: Frank was pleased when Bill said that he was the winner of the competition. Here, the word “he” could refer equally well to Frank or Bill [4, Section ‘Pitfall 2’].
A comprehensive solution to the problems posed by WSIs depends on two things: 1) An ability to learn relevant syntax and semantics, including knowledge of the world like the “sophisticated knowledge of councilmen, demonstrators, and politics” noted by Winograd, and 2) An ability to make use of that syntactic and semantic knowledge in the interpretation of WSIs.
2.2 The SP System
The SP System—meaning the SP Theory of Intelligence and its realisation in terms of the SP Computer Model—has been under development since about 1987, with a break between early 2006 and late 2012. There is an outline of the SP System in Appendix A. Since an understanding of the evidence and arguments presented in this paper depend on an understanding of the workings of the SP System, readers who are not already familiar with the system are urged to read Appendix A before reading the rest of the paper.
As noted in Appendix A
, the overarching goal in the development of the SP System has been to create a system that can simplify and integrate observations and concepts across artificial intelligence, mainstream computing, mathematics, and human learning, perception, and cognition.
To a large extent, this quest has been successful, as outlined in Appendix A. The SP System combines relative simplicity with versatility in diverse aspects of intelligence (Appendix A.5.1), versatility in the representation of diverse kinds of knowledge (Appendix A.5.2), and the seamless integration of diverse aspects of intelligence and diverse kinds of knowledge in any combination (Appendix A.5.3). And it has several potential benefits and applications (Appendix A.5.4).
As indicated in Section 2.1, the main focus of this paper is on how the SP System may function in the interpretation of WSs, with relatively little to say about the learning of relevant syntax and semantics. However, for reasons given in Appendix A.3, it is anticipated that, when the learning capabilities of the SP Computer Model have been further developed for the unsupervised learning of natural language syntax, those capabilities will generalise with little or no modification to the learning of semantic structures and the learning of structures in which syntax and semantics are integrated.
2.2.1 Evaluation of the SP System in terms of simplicity and power
A major strength of the SP System is the way that it combines conceptual simplicity with high levels of explanatory and descriptive power (Appendix A.5). This has a bearing on how the system may be evaluated in terms of its performance in the interpretation of WSs.
As we shall see with the examples in Sections 3.1, 3.2, and 3.3, the SP System, with appropriate data, can provide robust interpretations of WSs, in accordance with what people judge to be correct. These interpretations are achieved with the SP Computer Model as it was developed to meet its original objectives, and without any adaptation or modification of any kind.
This means that, in terms of ‘simplicity’ and ‘power’ (Appendix A.1), the discovery that the SP System can achieve robust interpretations of WSs without any adaptation or modification means that the simplicity of the system is the same as before, but (our knowledge of) its descriptive and explanatory power has been increased. Thus, in terms of Ockham’s razor, and in terms of our knowledge of the system and what it can do, the SP System is more plausible than before.
By contrast, any system that has been developed as an ad hoc solution to the problem of interpreting WSs is likely to be much less plausible than the SP system because it will not compete with the SP system in other aspects of AI.
2.3 Related research
There is now a large amount written about WSs, too much to be described exhaustively in this paper. Hence, this section presents a selective review, concentrating on more recent studies.
Hector Levesque 
presents an alternative to the Turing Test that involves responding to typed English sentences, like the Turing Test. But, unlike the Turing Test, the AI taking the test is not required to engage in a conversation and fool an interrogator into believing that he or she is dealing with a person. Instead, this WSC requires the AI to disambiguate WSIs. Levesque suggests that it is reasonable to believe that: “with a very high probability, anything that answers [a WSC] correctly is engaging in behaviour that we would say shows thinking in people.” and he adds: “Whether or not a subject that passes the test is really and truly thinking is the philosophical question that Turing sidesteps.” (ibid., Discussion and Conclusion).
There is more about the WSC and associated issues in . In that paper, the authors make a connection between the study of WSs and the study of commonsense knowledge (and, by implication, commonsense reasoning): “… we believe that in order to pass the [WSC], a system will need to have commonsense knowledge about space, time, physical reasoning, emotions, social constructs, and a wide variety of other domains. Indeed, we hope that the [WSC] will spur new research into representations of commonsense knowledge.” (ibid
., p. 558). But they add: “However, nothing in the [WSC] insists on this approach, and we would expect researchers [in natural language processing] to try different approaches.” (ibid.).
Leora Morgenstern and Charles Ortiz  describe the WSC competition, now run roughly once a year and sponsored by Nuance Communications, Inc., to encourage efforts to develop programs that can correctly interpret WSs. The first of these events was run on July 11, 2016, at the International Joint Conference on Artificial Intelligence (IJCAI-16). “The first round of the challenge was a collection of 60 PDPs [Pronoun Disambiguation Problems]. The highest score achieved was 58% correct, by Quan Liu, from University of Science and Technology, China. Hence, by the rules of that challenge, no prizes were awarded, and the challenge did not proceed to the second round.” (from bit.ly/2R4gSFJ).
Altaf Rahman and Vincent Ng  examine the task of determining (‘resolving’) the meanings of pronouns in sentences where there are no obvious clues from the syntax—much as in the WSC. They present results from a “Combined Resolver”—a combination of the “Stanford resolver” and the “Baseline Ranker”—which “significantly outperforms state-of-the-art resolvers” but has “a lot of room for improvement” (ibid., Section 5.4).
In a paper entitled “On our best behaviour”, Hector Levesque  discusses some some general issues relating to the WSC including: “… what does it tell us when a good semblance of a behaviour can be achieved using cheap tricks that seem to have little to do with what we intuitively imagine intelligence to be?” and “… are the philosophers right, and is a behavioural understanding of intelligence simply too weak?” He suggests that both those ideas are wrong and that “… we should put aside any idea of tricks and short cuts, and focus instead on what needs to be known, how to represent it symbolically, and how to use the representations.” (ibid., p. 34, emphasis in the original). Two main hurdles need to be overcome: much of what we know comes via language, but we need knowledge to interpret language; and even at the level of what is known by children, there appears to be much complexity and heavy computational demands.
With respect to the WSC, Peter Schüller  considers pairs of sentences like these: Sam’s drawing was hung just above Tina’s and it did look much better with another one [below / above] it. Here, people naturally assume that “another one” is Sam’s drawing or Tina’s, although it could be a third drawing by someone else. He suggests that what people naturally assume may be explained in terms of “Relevance Theory” and develops these ideas with a simplified version of Roger Schank’s graph framework for natural language understanding.
Daniel Bailey and colleagues , in discussing the problem of interpreting WSs, say that “we treat coreference resolution as a by-product of a general process of establishing discourse coherence: a resolution for a pronoun is acceptable if it makes the discourse ‘coherent’.” (p. 17). Later, they explain that, in a sentence like Joan made sure to thank Susan for all the help she had given, the phrases Joan made sure to thank Susan and Susan had given help
“are correlated in the sense that either one would cause the hearer to view the other as more plausible.” (p. 18). They go on to present a “correlation calculus” for representing and reasoning about such relationships which, although it is not founded on statistical concepts of correlation, “Nevertheless, our correlation calculus turned out to be closely related to correlation in the sense of probability theory …” (p. 18).
Ali Emami and colleagues  propose a three-stage knowledge hunting method for interpreting any given WSI: 1) Perform a partial parse of the WSI to isolate the main elements of the meaning; 2) Generate queries to send to a search engine in order to extract text snippets that resemble the given WSI; 3) Obtain a set of text snippets that resemble the given WSI, and use this information to resolve the ambiguity in the WSI. They say that their method compares well with AI alternatives but is not as good as a person.
Adam Richard-Bollans and colleagues 
consider the WSC as a means for highlighting problems in the field of commonsense reasoning. Approaches that they discuss include machine learning approaches and ‘commonsense rules’. Key challenges include: pragmatics (extra-linguistic factors, such as context, and how they allow the understanding of a speaker’s intended meaning), assumptions about the world (e.g., if we throw something down to someone, that person must be below you), and the level of detail or vagueness that may be needed in formalising commonsense knowledge. They propose an alternative approach, with knowledge bases for the meanings of commonsense terms and the use of heuristics based on pragmatics.
Arpit Sharma and colleagues [14, 15] present an approach that identifies the knowledge needed to answer a challenge question, hunts down that knowledge from text repositories, and then reasons with the knowledge and the question to come up with an answer. This research includes the development of a semantic parser. They show that their approach works well on a subset of Winograd schemas.
3 Examples of how the SP System may disambiguate WSIs
The three subsections that follow present three pairs of WSIs, each one with an SP-multiple-alignment produced by the SP Computer Model that demonstrates how the ambiguity in the sentence may be resolved.
A feature of the SP Computer Model is that it has a tendency to produce SP-multiple-alignments that are very large and cannot easily be fitted on one page. Quite often it is possible to work around this problem by choosing suitable examples or splitting SP-multiple-alignments into two or more parts. But with these examples, even with the choice of relatively short WSIs, those work-arounds are not possible—so it has been necessary to do something different.
The solution that has been adopted with these examples is that each SP-multiple-alignment has been produced at full size in vector-graphic form in a PDF file, and then shrunk to a size that will fit on a page. Then, providing each SP-multiple-alignment is viewed on a computer, it may be magnified to whatever size makes it legible, and it will be sharp at any size because of the vector-graphic encoding. For the convenience of readers, the figures are available in a separate file (‘sp_ws_figures.pdf’), in addition to their display in the body of this paper. That means that the figures in the separate file may be magnified without magnifying the main body of the paper.
A point to note about these examples is that, although the words ‘syntax’ and ‘semantics’ are used in discussing the examples, the SP System makes no formal distinction between the two. In the SP System, both ‘syntax’ and ‘semantics’ are information and may be combined flexibly without reference to any informal classification we may apply to them.
It should be stressed again that, up to now in this research, there has been no attempt to apply any kind of learning processes. In each of the examples to be described, the New SP-pattern, and all the Old SP-patterns, have been supplied ready-made to the SP Computer Model (see also Section 3.4).
It is likely that there is much room for debate about the details of these examples. But any such concerns should not distract from the main point of the examples: that within the framework of the SP system, and with WSIs containing a pronoun that requires disambiguation, it is relatively straightforward to discover the referent of such a pronoun.
All the WSIs in what follows contain at least one capital letter. But in the sentences provided as New patterns for the SP Computer Model, all capital letters have been replaced with their lower-case equivalents. This is to by-pass rules for capitalisation which might otherwise be a distraction from the main point of these examples: how to find the referent for the pronoun in each example.
3.1 The city councilmen refused the demonstrators a permit
This subsection is concerned with Terry Winograd’s [18, p. 33] two example sentences:222Apart from one difference, this is the first example in the ‘Collection of Winograd Schemas’, compiled by Ernest Davis and colleagues, and shown on bit.ly/2MPm64B, retrieved 2018-09-26. The difference is to use exactly the same two sentences presented by Winograd [18, p. 33] which, at their ends, have [‘feared violence’/‘advocated revolution’] instead of [‘feared violence’/‘advocated violence’].
The city councilmen refused the demonstrators a permit because they feared violence and
The city councilmen refused the demonstrators a permit because they advocated revolution
In each case, the sentence is supplied as a New SP-pattern to the SP Computer Model together with a collection of Old SP-patterns which describe the syntax and semantics of the given sentence and other sentences of that kind.
3.1.1 The city councilmen … feared violence
With the first sentence, the best SP-multiple-alignment created by the SP Computer Model is shown in Figure 1. Here, the word ‘best’ means that, out of the many SP-multiple-alignments created by the SP Computer Model, the given SP-multiple-alignment is the one in which the New SP-pattern may be encoded most economically in terms of the Old SP-patterns in that SP-multiple-alignment, as described in [21, Section 4.1] and [19, Section 3.5].
The SP-multiple-alignment shown in Figure 1 is, if effect, a parsing of the sentence the city councilmen refused the demonstrators a permit because they feared violence, much like the parsing in Figure 10, except that SP-symbols in the sentence are whole words instead of letters as in the sentence in Figure 10 and, as described in Appendix B, the SP-multiple-alignment in Figure 1, like other examples in this paper, attempts to marry syntax with semantics. It has been moved into Appendix B because it is quite tentative and is not relevant to the main substance of this paper—how to disambiguate pronouns in WSIs. Readers may safely ignore it if they wish.
3.1.2 Finding what ‘they’ refers to
Of course, the main point of interest with this example is how it determines the referent for the word “they” in the city councilmen refused the demonstrators a permit because they feared violence. This disambiguation is achieved via the SP-pattern ‘textttPEACE_LOVING PN #PN v1 n0’ which appears in column 21 in Figure 1. The connection is made correctly because, within that SP-pattern:
The SP-symbol ‘textttPEACE_LOVING’ is aligned with the same symbol in the SP-pattern ‘textttN n3 councilmen COUNCILMEN PEACE_LOVING #N’ in column 14, which, in the light of the next bullet point, identifies ‘textttcouncilmen’ and its associated meaning as the referent for “they” in the given sentence.
The SP-symbols ‘textttPN #PN’ are aligned with the matching SP-symbols in ‘textttNP np1 PN #PN #NP’ (column 9) and in ‘textttPN pn2 they THEY #PN’ (column 8), thus identifying the pronoun “they”.
The SP-Symbol ‘textttv1’ matches the same symbol in ‘textttV v1 feared FEARED #V’ in column 10, thus identifying the word “feared” and its associated meaning.
And the SP-Symbol ‘textttn0’ matches the same symbol in ‘textttN n0 violence VIOLENCE #N’ in column 19, thus identifying the word “violence” and its associated meaning.
In short, within the SP-multiple-alignment shown in Figure 1, the SP-pattern ‘textttPEACE_LOVING PN #PN v1 n0’ has the effect of highlighting the association between peace-loving councilmen, the pronoun ‘they’, and the councilmen’s probable fear of violence.
As mentioned near the beginning of Section 3, there is plenty of room for debate about the grammatical details of these examples. Much the same goes for the proposed solution to the WS problem where several variations are possible. But, as before, any such variations should not distract from the key point: that, within the framework of the SP System, and with appropriate SP-patterns, finding the referent for a pronoun in a WSI is relatively straightforward.
As an illustration of one possible variant of the solution described in Section 3.1.2, Figure 2 shows how the … feared violence sentence may be disambiguated via the creation of an SP-multiple-alignment, much as in Figure 1, but with the SP-pattern ‘textttPEACE_LOVING PN #PN FEARED VIOLENCE’ in column 21 instead of ‘textttPEACE_LOVING PN #PN v1 n0’.
Another possible variant is shown in Figure 3. Here, Old SP-patterns have been supplied to the SP Computer Model which, in a simple way, introduce the concept of class-inclusion hierarchy and the inheritance of attributes.
In the figure, the ‘PEACE_LOVING’ attribute, contrary to fact, appears in a new SP-pattern for ‘democratic politicians’, ‘DP dp0 democratic_politicians PEACE_LOVING #DP’, in column 11. And ‘PEACE_LOVING’ is aligned with the same symbol in the SP-pattern ‘PEACE_LOVING PN #PN FEARED VIOLENCE’ in column 22, much as in Figure 2. The new SP-pattern, for ‘democratic politicians’ connects with a modified SP-pattern for ‘councilmen’, ‘N n3 councilmen COUNCILMEN DP #DP #N’, in column 10. The overall effect is that, in the manner of object-oriented programming, the class ‘councilmen’ inherits the ‘peace loving’ attribute from the more general class ‘democratic politicians’.
3.1.4 The demonstrators … advocated revolution
The second of Winograd’s  WSIs, The city councilmen refused the demonstrators a permit because they advocated revolution, may be processed in a similar way. Figure 4 shows the best SP-multiple-alignment created by the SP Computer Model with the given sentence as the New pattern and the same set of Old SP-patterns as before. This time, the SP-pattern ‘textttRADICAL_CHANGE PN #PN v2 n1’, which appears in column 21, has the effect, in much the same manner as before, of highlighting the association between the demonstrators and their probable interest in radical change, the pronoun ‘they’, and the demonstrator’s advocacy of revolution.
3.2 Pete envies Martin
The second pair of sentences to be considered are: Pete envies Martin [because/although] he is very successful.333this is the 20th example in the ‘Collection of Winograd Schemas’, compiled by Ernest Davis and colleagues, and shown on bit.ly/2MPm64B, retrieved 2018-09-26.
3.2.1 Pete envies Martin because …
Figure 5 shows the best SP-multiple-alignment produced by the SP Computer Model with pete envies martin because he is very successful as a New SP-pattern, which appears in column 0, and a collection of Old SP-patterns describing the syntax and semantics of that kind of sentence, some of which appear in columns 1 to 22, one SP-pattern per column.
In a manner much like the examples in Section 3.1, disambiguation is achieved via an SP-pattern that connects relevant parts of the SP-multiple-alignment. Here, that SP-pattern is ‘pat_a #pat_a c0 HE INT #INT SUCCESSFUL’ which appears in column 15 in the figure. In that SP-pattern:
The pair of SP-symbols ‘pat_a #pat_a’, which are mnemonic for ‘patient’, are aligned with matching symbols in the SP-pattern in column 4 which span the structure in columns 2, 1, and 0, which identify ‘martin’ as having the semantic role of ‘patient’ in the given sentence.
The SP-symbol ‘c0’ is aligned with the matching SP-symbol in column 7, thus identifying the special word ‘because’ in ‘Cn c0 because BECAUSE #Cn’.
The SP-symbol ‘HE’ is aligned with the matching SP-symbol within the SP-pattern ‘PN pn0 he HE #PN’ in column 12.
The pair of SP-symbols ‘INT #INT’ are aligned with matching SP-symbols within the SP-pattern ‘INT int0 very #INT’ in column 14.
And the SP-symbol ‘SUCCESSFUL’ is aligned with the matching SP-symbol within the SP-pattern ‘ADJ adj3 successful SUCCESSFUL #ADJ’ in column 9.
In short, the SP-pattern ‘pat_a #pat_a c0 HE INT #INT SUCCESSFUL’ has the effect of identifying ‘martin’ as the referent of ‘he’ within the given sentence, with the other SP-symbols within the SP-pattern, especially the special word ‘because’, providing the necessary context.
3.2.2 Pete envies Martin although …
Figure 6 shows the best SP-multiple-alignment produced by the SP Computer Model with pete envies martin although he is very successful as a New SP-pattern, which appears in column 0, and a collection of Old SP-patterns describing the syntax and semantics of that kind of sentence, some of which appear in columns 1 to 22, one SP-pattern per column.
As before, there is a key SP-pattern which identifies the referent for the pronoun ‘he’ in the given sentence. Here, that SP-pattern is ‘agnt_a #agnt_a c2 HE INT #INT SUCCESSFUL’ which appears in column 15 of the figure. By contrast with the example in Section 3.2.1, the pair of SP-symbols ‘agnt_a #agnt_a’ are aligned with matching symbols in column 4 which have the effect of marking ‘pete’ as an object of interest. In much the same way as in the example in Section 3.2.1, ‘pete’ is identified as the referent of ‘HE’.
3.3 The fish ate the worm
The third example to be considered is: The fish ate the worm. It was [tasty/hungry].444this is the 52nd example in the ‘Collection of Winograd Schemas’, compiled by Ernest Davis and colleagues, and shown on bit.ly/2MPm64B, retrieved 2018-09-26.
3.3.1 The worm … tasty
Figure 7 shows the best SP-multiple-alignment produced by the SP Computer Model with the fish ate the worm it was tasty as a New SP-pattern, which appears in column 0, and a collection of Old SP-patterns describing the syntax and semantics of the two target sentences. Some of those SP-patterns are shown in columns 1 to 21, one SP-pattern per column.
As readers may guess, the solution in this case is similar to what has presented in previous examples. In this case, the key SP-pattern is ‘PREY PN #PN adj2’. The first SP-symbol, ‘PREY’ matches the same SP-symbol in the SP-pattern ‘N n1 worm WORM PREY #N’ in column 1, thus marking ‘worm’ as an object of interest. The pair of SP-symbols ‘PN #PN’ match the same two SP-symbols in column 12 and in the SP-pattern ‘PN pn2 it IT #PN’ thus identifying ‘it’ as a pronoun. And the SP-symbol ‘adj2’ selects the SP-pattern ‘ADJ adj2 tasty TASTY #ADJ.
In short, the SP-pattern ‘PREY PN #PN adj2’ tells us that the ‘worm’ is the referent of the pronoun ‘it’ because, as a kind of prey for animals like fish, it can be ‘tasty’.
3.3.2 The fish … hungry
Figure 8 shows the best SP-multiple-alignment produced by the SP Computer Model with the fish ate the worm it was hungry as a New SP-pattern, which appears in column 0, and a collection of Old SP-patterns describing the syntax and semantics of the two target sentences. Some of those SP-patterns are shown in columns 1 to 21, one SP-pattern per column.
In much the same way as in Section 3.3.1, the SP-pattern ‘PREDATOR PN #PN adj1’ makes a connection between the ‘fish’, the pronoun ‘it’ and the fact that the fish was ‘hungry’.
3.4 The potential of unsupervised learning
As noted in Section 3, each of the SP-multiple-alignments presented in this paper has been created by the SP Computer Model with with a collection of SP-patterns supplied by the user: one New SP-pattern and a repository of Old SP-patterns including those that appear in the given SP-multiple-alignment. This is because unsupervised learning in the SP Computer Model has shortcomings (Appendix A.3) which mean that it is not yet good enough for demonstrating how the SP System can learn the knowledge needed for disambiguating WSIs.
However, a comprehensive account of how WSIs may be disambiguated should include an account of how relevant knowledge may be learned. In the light of what has already been learned about the strengths and weaknesses of unsupervised learning in the SP Computer Model as it is now, and how the weaknesses may be overcome (Appendix A.3), here are some observations about how the system may be developed to learn the kind of knowledge needed for the disambiguation of WSIs:
It is anticipated that it should be relatively straightforward to develop the SP System for the learning of segmental structures (words and phrases) and classes of such structures (e.g., nouns, verbs, and adjectives). As noted in Appendix A.3, the main hurdle to be overcome is the learning of structures at intermediate levels (between words and sentences) such as phrases and clauses.
Likewise, it should be feasible to develop the system for the learning of discontinuous dependencies such as plurality dependencies or gender dependencies in syntax (more below). As with segmental structures, this is a weakness of the SP Computer Model as it is now (Appendix A.3).
More challenging will be the learning of non-syntactic ‘semantic’ knowledge of the world, mainly because it will be necessary to generalise the system for the learning of two-dimensional and three-dimensional structures, and the learning of ‘commonsense’ knowledge of time, speed, distance, and the like.
In connection with the problem of finding the referent of a pronoun in a WSI, an SP-pattern like ‘textttPEACE_LOVING PN #PN v1 n0’ in column 21 in Figure 1 is particularly important (Section 3.1.2), and likewise for the SP-pattern ‘textttPEACE_LOVING PN #PN FEARED VIOLENCE’ in column 21 in Figure 2 (Section 3.1.3).
The importance of SP-patterns like these is that they provide connections between things like ‘textttPEACE_LOVING’, ‘textttPN #PN’, ‘textttFEARED’, and ‘textttVIOLENCE’, which may be and usually are separated from each other by other things. It is precisely the ability to learn discontinuous dependencies which is required to learn those kinds of SP-patterns.
The method that is proposed in this paper for finding the referent for a pronoun in a WSI relies in part on a rather simple principle: that any person or group of people that is ‘peace loving’ is also likely to ‘fear violence’, and likewise for the association between a person or group having an interest in ‘radical change’ and a willingness to ‘advocate revolution’, and so on. The concept of SP-multiple-alignment within the SP Computer Model provides a means for this kind of association to exert its influence across intervening structures without disruption or disturbance by those intervening structures.
The essential simplicity of this idea seems to be in conflict with Terry Winograd’s suggestion that resolving the ambiguity in each of his example sentences requires a “sophisticated knowledge of councilmen, demonstrators, and politics” [18, p. 33]. Is this a genuine conflict or is there some way in which the two views may be reconciled? The suggestion here is that they can indeed be reconciled, something like this:
It is likely that, in real life, most adults will indeed have a sophisticated knowledge of councilmen, demonstrators, and politics, and this knowledge will indeed be applied in the task of determining the referent of “they” in sentences like The city councilmen refused the demonstrators a permit because they feared violence. Their knowledge may, for example, contain many class-inclusion hierarchies like that shown in Figure 3 in Section 3.1.3.
As we have seen in each of the examples presented in Section 3, short identifiers are sufficient for determining the referent of the pronoun in each WSI. In more realistic examples, most such identifiers would each be a label or ‘code’ for a relatively complex chunk of information.
In short, the method that has been proposed in this paper for determining the referent of a pronoun in a WSI will work with short identifiers, but in more realistic settings, it is likely that most such identifiers would be associated with relatively complex bodies of knowledge.
In ‘Winograd Schema’ kinds of sentence like The city councilmen refused the demonstrators a permit because they feared violence and The city councilmen refused the demonstrators a permit because they advocated revolution it is easy for people to decide what “they” refers to but it can be challenging for AI systems [18, p. 33]. This paper describes with examples how, with the SP Theory of Intelligence and its realisation in the SP Computer Model, outlined in an Appendix, and with user-supplied information about relevant syntax and semantics, these kinds of problem of interpretation may be solved.
With the first sentence as an example, the key to finding what “they” refers to is: 1) to provide some information about one or more features of city councilmen such as, for example, that they value peace in their city; 2) to provide a means of recording the association between ‘peace loving’ and ‘fear of violence’; and 3) to connect “they” into that association.
At present, this kind of information, and other relevant information about syntax and semantics, must be supplied to the SP System at the outset. But a comprehensive AI solution to these kinds of problem depends on an ability of the SP System, or any other kind of AI system, to learn relevant syntax and semantics for itself.
Existing strengths and weaknesses of the SP System in the unsupervised learning of English-like artificial languages suggest that it is not yet good enough to learn the kinds of syntactic and semantic knowledge that is needed to solve Winograd Schema types of problem, but there is clear potential for unsupervised learning in the SP System to be developed to a point where it can learn such knowledge for itself. In particular, there is clear potential for it to learn the kinds of association described under point (2) in the last-but-one paragraph—a kind of association which is similar to the kinds of discontinuous association in syntax—bridging intervening kinds of structure—which are found in most natural languages.
Appendix A Outline of the SP system
The SP System—which means the SP Theory of Intelligence and its realisation in the SP Computer Model—is the product of an extended programme of research, seeking to simplify and integrate observations and concepts across artificial intelligence, mainstream computing, mathematics, and human learning, perception, and cognition, with information compression as a unifying theme. Despite its ambition, this objective has been largely met, as summarised in Appendix A.5, below.
The SP System is conceived as a brain-like system that receives New information through its senses and stores some or all of it as Old information, as shown schematically in Figure 9.
In the SP System, all kinds of information or knowledge are represented in arrays of atomic SP-symbols in one or two dimensions called SP-patterns. At present, the SP Computer Model works only with one-dimensional SP-patterns but it is envisaged that it will be generalised to work with two-dimensional SP-patterns. And at present, an SP-symbol is an ASCII character, or a string of such characters bounded by spaces or the end of the SP-pattern in which it appears.
a.1 Information compression, Ockham’s razor, ‘simplicity’, and ‘power’
Information compression, mentioned above, may be seen to be equivalent to a process of maximising the Simplicity of any given body of information, I, by extraction of redundancy from I, whilst retaining as much as possible of its descriptive Power. Hence the name ‘SP’.
Given that equivalence, information compression may be seen to have a two-fold significance in the SP programme of research:
Simplification and integration of observations and concepts across a broad canvass (the overarching goal of the SP research) is, in accordance with Ockham’s razor, a process of developing a system that combines conceptual Simplicity of the system with high levels of explanatory or descriptive Power.
Information compression is central in the workings of the SP System. In that connection, we can make a broad distinction between two kinds of processes in the SP System:
The building of SP-multiple-alignments. The building of SP-multiple-alignments in the SP System, described in Section A.2, is a powerful means of compressing New information from the SP System’s environment. It is also the key to the SP System’s strengths in most aspects of intelligence, but with additional processing in unsupervised learning (next).
Unsupervised learning. The process of unsupervised learning in the SP System (Appendix A.3) is another means of compressing information which incorporates the building of SP-multiple-alignments but which also includes a process of building one or more SP-grammars, meaning collections of Old SP-patterns which are relatively effective in the compression of a given set of New SP-patterns.
The reason that information compression has been adopted as a unifying principle in the workings of the SP System is because of abundant evidence for the importance of information compression in human learning, perception, and cognition . The success of the system in modelling several aspects of human intelligence (Appendix A.5.1) provides corroborating evidence for the importance of information compression in human cognition.
A last point to mention in this connection is that it has been known for some time that there is an intimate relation between information compression and concepts of inference and probability [13, 16, 17, 7]. This makes it relatively straightforward for the SP System to calculate probabilities for inferences made by the system ([21, Section 4.4], [19, Section 3.7]).
The concept of SP-multiple-alignment in the SP System, which has been borrowed and adapted from the concept of ‘multiple sequence alignment’ in bioinformatics, means the arrangement of two or more SP-patterns alongside each other, and the ‘stretching’ of SP-patterns in a computer so that matching symbols are brought into line.
An example of an SP-multiple-alignment, created by the SP Computer Model, is shown in Figure 10. This is the best SP-multiple-alignment produced by the SP computer model with: a New SP-pattern, ‘f o r t u n e f a v o u r s t h e b r a v e’ shown in column 0, representing a sentence to be parsed; and a repository of user-supplied Old SP-patterns representing grammatical categories, including morphemes and words. Some of those Old SP-patterns appear in columns 1 to 9 of the figure, one SP-pattern per column.
Here, the meaning of ‘best’ is that the given SP-multiple-alignment is the one which allows the New SP-pattern to be encoded most economically in terms of the Old SP-patterns in the SP-multiple-alignment, as described in [21, Section 4.1] and [19, Section 3.5].
For any given New pattern and collection of Old SP-patterns, the number of possible SP-multiple-alignments is normally too large to be searched exhaustively. Hence, the SP Computer Model uses heuristic techniques which can normally find SP-multiple-alignments that are reasonably good, and may quite often be theoretically ideal, but which cannot guarantee to find such ideal SP-multiple-alignments.
a.3 Unsupervised learning
As mentioned in Appendix A.1 above, unsupervised learning in the SP System incorporates the building of SP-multiple-alignments but, in addition, there is a process of creating one or more SP-grammars, meaning collections of Old SP-patterns which are relatively good for the economical encoding of a given set of New SP-patterns.
The reason that, with respect to learning, the SP research is concentrating on the development of unsupervised
learning—meaning learning without assistance from a ‘teacher’ or anything equivalent—is because it appears that most human learning is unsupervised, and because of the belief that unsupervised learning can provide the foundation of other kinds of learning such as ‘supervised learning’, ‘reinforcement learning’, ‘learning by being told’, ‘learning by imitation’, and so on.
The main framework for unsupervised learning has been established in the SP Computer Model. It has already demonstrated an ability to discover generative grammars from unsegmented samples of English-like artificial languages, including segmental structures, classes of structure, and abstract patterns. But it has shortcomings summarised in [21, Section 3.3]. How the system may be developed is outlined here:
The learning of segmental structures. The SP Computer Model has already demonstrated an ability to learn segmental structures such as words from data in which significant segments are not marked (Appendix A.3). Thus it has clear potential to learn such things as words and more abstract structures such as sentences. But a weakness of the model as it is now is that it does not learn structures at intermediate levels such as phrases and clauses (ibid.). It is anticipated that this problem will prove to be soluble.
The learning of class-inclusion structures. Much the same may be said about the learning of class-inclusion structures such as nouns, verbs, adjectives, and so on. The SP Computer Model can learn such groupings at an abstract level but cannot learn structures at intermediate levels. As before, it is anticipated that this problem will prove to be soluble.
The learning of discontinuous dependencies. Another shortcoming in how the SP Computer Model learns is that it cannot yet learn discontinuous dependencies in syntax such as gender dependencies (masculine or feminine) in a language like French (Appendix A.3). As before, it anticipated that this problem will prove soluble.
The learning of semantic structures. An overarching goal in the SP programme of research is that structures and processes in the SP System should be applicable across a broad canvass including artificial intelligence, mainstream computing, mathematics, and human learning, perception, and cognition. In accordance with that principle, it is anticipated that, if the kinds of learning described in the previous three bullet points can be developed for the learning of syntax, they will prove to be applicable to the learning of ’semantic’ structures, meaning knowledge of the non-syntactic world. The main change that will be needed will be generalisation of the SP System for SP-patterns in two dimensions, which will facilitate the learning of structures in three dimensions [22, Sections 6.1 and 6.2]. And there will need to progress in the learning of ‘commonsense’ knowledge of the kinds described by .
The integration of syntax and semantics. Probably the most challenging problem to be solved is to develop the SP System to a stage where it can learn plausible structures that integrate both natural language syntax and the non-syntactic knowledge that provides the semantics of natural language.
is a version of the SP System expressed in terms of neurons and their inter-connections11] and is likely to share the several advantages of the SP System compared with deep learning ([27, Section V], ). SP-Neural has potential as a source of hypotheses in neuroscience and as a guide to explorations in that field.
a.5 Strengths and potential of the SP System
In accordance with Ockham’s razor (Appendix A.1), the SP System combines conceptual Simplicity with high levels of descriptive or explanatory Power, the latter summarised in the subsections that follow. Further information may be found in [21, Sections 5 to 12], [19, Chapters 5 to 9], , and in other sources referenced in the subsections that follow.
a.5.1 Versatility in aspects of intelligence
In the modelling of human-like intelligence, strengths of the SP System includes: unsupervised learning, the analysis and production of natural language; pattern recognition that is robust in the face of errors in data; pattern recognition at multiple levels of abstraction; computer vision; best-match and semantic kinds of information retrieval; several kinds of reasoning (next paragraph); planning; and problem solving.
With regard to reasoning, the strengths of the SP system include: one-step ‘deductive’ reasoning; chains of reasoning; abductive reasoning; reasoning with probabilistic networks and trees; reasoning with ‘rules’; nonmonotonic reasoning and reasoning with default values; Bayesian reasoning with ‘explaining away’; causal reasoning; reasoning that is not supported by evidence; the inheritance of attributes in class hierarchies and part-whole hierarchies. Where it is appropriate, probabilities for inferences may be calculated in a straightforward manner ([19, Section 3.7], [21, Section 4.4]).
a.5.2 Versatility in the representation of knowledge
Although SP-patterns are not very expressive in themselves, they come to life in the SP-multiple-alignment framework. Within that framework, they may serve in the representation of several different kinds of knowledge, including: the syntax of natural languages; class-inclusion hierarchies (with or without cross classification); part-whole hierarchies; discrimination networks and trees; if-then rules; entity-relationship structures [20, Sections 3 and 4]; relational tuples (ibid., Section 3), and concepts in mathematics, logic, and computing, such as ‘function’, ‘variable’, ‘value’, ‘set’, and ‘type definition’ ([19, Chapter 10], [24, Section 6.6.1], [29, Section 2]).
The addition of two-dimensional SP patterns to the SP computer model is likely to expand the representational repertoire of the SP system to structures in two-dimensions and three-dimensions, and the representation of procedural knowledge with parallel processing.
a.5.3 Seamless integration of diverse aspects of intelligence, and diverse kinds of knowledge, in any combination
An important third feature of the SP system, alongside its versatility in aspects of intelligence and its versatility in the representation of diverse kinds of knowledge, is that there is clear potential for the SP system to provide seamless integration of diverse aspects of intelligence and diverse kinds of knowledge, in any combination. This is because diverse aspects of intelligence and diverse kinds of knowledge all flow from a single coherent and relatively simple source: the SP-multiple-alignment framework.
It appears that seamless integration of diverse aspects of intelligence and diverse kinds of knowledge, in any combination, is essential in any artificial system that aspires to the fluidity, versatility and adaptability of the human mind.
Figure 11 shows schematically how the SP system, with SP-multiple-alignment centre stage, exhibits versatility and integration.
a.5.4 Potential benefits and applications of the SP system
Apart from its strengths and potential in modelling aspects of human intelligence, it appears that the SP System has several potential benefits and applications [30, Section 7]. These include: how the SP System may help solve nine problems with big data; the SP system opens up a radically new approach to the development of intelligence in autonomous robots; the SP System may form the basis for a database system with intelligence; the SP System may assist with medical diagnosis; the SP System may help in the development of computer vision and in the understanding of natural vision; SP-Neural may suggest hypotheses and avenues for research in neuroscience; the SP System has potential in the development of commonsense reasoning; other areas of application including : the simplification and integration of computing systems; applications of natural language processing; best-match and semantic forms of information retrieval; software engineering ; the representation of knowledge, reasoning, and the semantic web; information compression; bioinformatics; the detection of computer viruses; and data fusion; the concept of information compression via the matching and unification of patterns provides an entirely novel interpretation of mathematics  which is quite unlike anything described in existing writings about the philosophy of mathematics or its application in science and has several potential benefits and applications.
Appendix B Making connections between syntax and semantics
As mentioned in Section 3.1.1, the subject of this Appendix—the representation and processing of syntax and semantics in the example from that section and all other examples in this paper—is quite tentative and not relevant to the main substance of the paper—how WSIs may be disambiguated. Readers may safely ignore this Appendix if they wish.
By contrast with the SP-multiple-alignment in Figure 10, the SP-patterns in Figure 1 attempt to show in a simplified way, how, with the SP System, syntactic structures may be associated with corresponding semantic structures. For example:
Each word is represented by an SP-pattern like this: ‘N n3 councilmen COUNCILMEN PEACE_LOVING #N’ in column 14, where the lower-case string of characters ‘councilmen’ is intended to represent the surface form of the word, while the associated string of characters in capital letters, ‘COUNCILMEN’, is intended to represent, in a highly simplified form, the meaning of the word.
The SP-symbol ‘PEACE_LOVING’, which is discussed in Section 3.1.2, may be seen to be a supplement to, or part of, the semantic information associated with ‘councilmen’.
The other symbols, ‘N’, ‘n3’, ‘#N’ in ‘N n3 councilmen COUNCILMEN peace_loving #N’, are grammatical categories, much as in the SP-patterns in Figure 10.
The SP-pattern ‘Sa agnt_a NP #NP #agnt_a act_a V #V #act_a pat_a NP #NP #pat_a obj_a NP #NP #obj_a actionA agentA patientA objectA #Sa’ in column 7 is intended to represent both the syntax and semantics of ‘the city councilmen refused the demonstrators a permit’.
Here, the first part of the pattern, ‘agnt_a NP #NP #agnt_a act_a V #V #act_a pat_a NP #NP #pat_a obj_a NP #NP #obj_a’ is largely concerned with syntax, while ‘actionA agentA patientA objectA’ is largely about semantics. Notice that the order of ‘agnt_a ... #agnt_a act_a ... #act_a pat_a ... #pat_a obj_a ... #obj_a’ (meaning ‘agent, action, patient, object’) in the ‘syntax’ part is different from ‘actionA agentA patientA objectA’ (‘action, agent, patient, object’) in the ‘semantics’ part.
In a similar way, the SP-pattern ‘Sb agnt_b NP #NP #agnt_b act_b V #V #act_b obj_b NP #NP #obj_b actionB agentB objectB #Sb’ in column 11 is intended to represent both the syntax and semantics of ‘they feared violence’. Here, the first part of the pattern, ‘Sb agnt_b NP #NP #agnt_b act_b V #V #act_b obj_b NP #NP #obj_b’ (‘agent’, ‘action’, ‘object’) is largely concerned with syntax, while ‘actionB agentB objectB’ (‘action’, ‘agent’, ‘object’) is largely about semantics, and the ordering is different in the two cases.
In English and many other languages, a given idea may often be expressed in more than one way. For example, the meaning of John hit the ball is essentially the same as The ball was hit by John. This suggests that there is a single semantic structure that may be expressed via two or more surface structures and that, for at least one of those surface structures, perhaps all of them, there is a process of mapping the surface structure on to the underlying semantic structure.
With the SP-multiple-alignment shown in Figure 1, that kind of mapping may be achieved like this:
With the SP-pattern in column 27, ‘agnt_a #agnt_a agentA’:
The pair of SP-symbols ‘agnt_a #agnt_a’ in column 27 are aligned with matching symbols in column 7 that bridge the pair of symbols ‘NP #NP’ in that column, thus identifying the noun phrase ‘the city councilmen’.
The SP-symbol ‘agentA’ in column 27 is aligned with the matching symbol in column 7.
The overall effect is to make a connection between ‘the city councilmen’ and ‘agentA’.
There is a similar mapping of symbols: in ‘act_a #act_a actionA’ in column 28 to symbols in column 7; in ‘pat_a #pat_a patientA’ in column 23 to symbols in column 7; and in ‘obj_a #obj_a objectA’ in column 22 to symbols in column 7.
The overall effect is to map the surface form ‘the city councilmen refused the demonstrators a permit’ (‘actor’, ‘action’, ‘patient’, ‘object’) into the form (‘actionA’, ‘agentA’, ‘patientA’, ‘objectA’) in column 7, which may be regarded as a ‘semantic’ version of the surface form.
In a similar way, the surface form ‘they feared violence’ may be seen to be mapped into the semantic form (‘actionB’, ‘agentB’, ‘objectB’) in column 11 via the SP-patterns ‘agnt_b #agnt_b agentB’ (column 25), ‘act_b #act_b actionB’ (column 26), and ‘obj_b #obj_b objectB’ (column 24).
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