On abstract modular inference systems and solvers

Yuliya Lierler,Miroslaw Truszczynski

doi:10.1016/j.artint.2016.03.004

Yuliya Lierler, Miroslaw Truszczynski

Open Access

https://doi.org/10.1016/j.artint.2016.03.004

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Abstract

Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience, and computational benefits. We introduce the concepts of abstract inference modules and abstract modular inference systems to study general principles behind the design and analysis of model generating programs, or solvers, for integrated multi-logic systems. We show how modules and modular systems give rise to transition graphs, which are a natural and convenient representation of solvers, an idea pioneered by the SAT community. These graphs lend themselves well to extensions that capture such important solver design features as learning. In the paper, we consider two flavors of learning for modular formalisms, local and global. We illustrate our approach by showing how it applies to answer set programming, propositional logic, multi-logic systems based on these two formalisms and, more generally, to satisfiability modulo theories.

Highlights

Knowledge representation and reasoning (KR) is concerned with developing formal languages and logics to model knowledge, and with designing and implementing corresponding automated reasoning tools
We introduce the concepts of abstract inference modules and abstract modular inference systems to study general principles behind the design and analysis of model-generating programs, or solvers, for integrated multilogic systems
More recent examples include constraint answer-set programming (CASP) [13] that integrates answer-set programming (ASP) [16, 18] with constraint modeling languages [22], and “multi-logic” formalisms PC(ID) [17], SM(ASP) [14] and ASP-FO [4] that combine modules expressed as logic theories under the classical semantics with modules given as answer-set programs

Summary

Introduction

Knowledge representation and reasoning (KR) is concerned with developing formal languages and logics to model knowledge, and with designing and implementing corresponding automated reasoning tools. Abstract inference modules S1 and S2 are equivalent if and only if they have the same models contained in the set σ(S1) ∪ σ(S2). We argued that theories and programs can be represented by equivalent abstract inference modules (Propositions 4 and 5).

Results

Conclusion