Relating Answer Set Programming and Many-sorted Logics for Formal Verification

TL;DR

This paper explores how translating Answer Set Programming into many-sorted first-order logic can improve formal verification by enabling modular reasoning, avoiding grounding, and utilizing automated theorem proving.

Contribution

It introduces alternative semantics for ASP based on translations into many-sorted first-order logic, enhancing modularity and verification capabilities.

Findings

Semantic translations enable modular reasoning in ASP.

Automated theorem provers can verify ASP properties.

The approach bypasses grounding limitations.

Abstract

Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy (especially, artificially intelligent) software systems. However, formally verifying ASP programs offers some unique challenges, such as 1. a lack of modularity (the meanings of rules are difficult to define in isolation from the enclosing program), 2. the ground-and-solve semantics (the meanings of rules are dependent on the input data with which the program is grounded), and 3. limitations of existing tools. My research agenda has been focused on addressing these three issues with the intention of making ASP verification an accessible, routine task that is regularly performed alongside program development. In this vein, I have investigated alternative semantics for ASP based on translations into the logic of here-and-there and many-sorted first-order logic. These semantics promote a modular understanding of logic programs, bypass grounding, and enable us to use automated theorem provers to automatically verify properties of programs.