
Generalizing inference systems by coaxioms
After surveying classical results, we introduce a generalized notion of ...
read it

Foundations of regular coinduction
Inference systems are a widespread framework used to define possibly rec...
read it

Unboxing Mutually Recursive Type Definitions in OCaml
In modern OCaml, singleargument datatype declarations (variants with a ...
read it

Flexible coinductive logic programming
Recursive definitions of predicates are usually interpreted either induc...
read it

Extending Coinductive Logic Programming with CoFacts
We introduce a generalized logic programming paradigm where programs, co...
read it

Flexible Coinduction in Agda
Theorem provers are tools that help users to write machine readable proo...
read it

Inductive supervised quantum learning
In supervised learning, an inductive learning algorithm extracts general...
read it
Coaxioms: flexible coinductive definitions by inference systems
We introduce a generalized notion of inference system to support more flexible interpretations of recursive definitions. Besides axioms and inference rules with the usual meaning, we allow also coaxioms, which are, intuitively, axioms which can only be applied "at infinite depth" in a proof tree. Coaxioms allows us to interpret recursive definitions as fixed points which are not necessarily the least, nor the greatest one, and classical results, which smoothly extend to this generalized framework, ensure the existence of such fixed points. This notion nicely subsumes standard inference systems and their inductive and coinductive interpretation, thus allowing formal reasoning in cases where the inductive and coinductive interpretation do not provide the intended meaning, or are mixed together.
READ FULL TEXT
Comments
There are no comments yet.