Strategy Logic with Imperfect Information

05/31/2018
by   Raphaël Berthon, et al.
0

We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii, and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, the problem turns out to be undecidable. We introduce a syntactical class of "hierarchical instances" for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications are concerned with finer observations of the model. We prove that model-checking SLii restricted to hierarchical instances is decidable. This result, because it allows for complex patterns of existential and universal quantification on strategies, greatly generalises previous ones, such as decidability of multi-player games with imperfect information and hierarchical observations, and decidability of distributed synthesis for hierarchical systems. To establish the decidability result, we introduce and study QCTL*ii, an extension of QCTL* (itself an extension of CTL* with second-order quantification over atomic propositions) by parameterising its quantifiers with observations. The simple syntax of QCTL* ii allows us to provide a conceptually neat reduction of SLii to QCTL*ii that separates concerns, allowing one to forget about strategies and players and focus solely on second-order quantification. While the model-checking problem of QCTL*ii is, in general, undecidable, we identify a syntactic fragment of hierarchical formulas and prove, using an automata-theoretic approach, that it is decidable. The decidability result for SLii follows since the reduction maps hierarchical instances of SLii to hierarchical formulas of QCTL*ii .

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

05/31/2018

Decidability results for ATL* with imperfect information and perfect recall

Alternating-time Temporal Logic (ATL*) is a central logic for multiagent...
07/30/2020

Reasoning about strategies on collapsible pushdown arenas with imperfect information

Strategy Logic with imperfect information (SLiR) is a very expressive lo...
05/31/2018

Reasoning about Knowledge and Strategies under Hierarchical Information

Two distinct semantics have been considered for knowledge in the context...
05/31/2018

Reasoning about Knowledge and Strategies

Two distinct semantics have been considered for knowledge in the context...
07/12/2016

Extended Graded Modalities in Strategy Logic

Strategy Logic (SL) is a logical formalism for strategic reasoning in mu...
07/19/2019

Provenance Analysis for Logic and Games

A model checking computation checks whether a given logical sentence is ...
02/21/2018

Playing with Repetitions in Data Words Using Energy Games

We introduce two-player games which build words over infinite alphabets,...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.