Technology Category
Constraint Satisfaction and Optimization: Satisfiability Modulo TheoriesKnowledge Representation and Reasoning: Logic ProgrammingReasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
SM-based Semantics for Answer Set Programs Containing Conditional Literals and Arithmetic
🤖 AI Summary
Existing semantics for nonmonotonic logic programs with conditional literals and arithmetic rely on infinite propositional translations and grounding, limiting expressiveness and analytical efficiency.
Method: This paper introduces, for the first time, a direct semantics that avoids both grounding and infinite-logic translations. Built upon the SM-operator framework, it models conditional literals as nested implications and integrates arithmetic constraints natively.
Contribution/Results: The semantics strictly generalizes the classical stable model semantics and is precisely equivalent to established semantics (e.g., Fages’, Ferraris’). It provides a concise, analyzable theoretical foundation for modern Answer Set Programming (ASP) extensions—including conditional literals and arithmetic—enabling more efficient solver design and formal verification.
Technology Category
Application Category
📝 Abstract
Modern answer set programming solvers such as CLINGO support advanced language constructs that improve the expressivity and conciseness of logic programs. Conditional literals are one such construct. They form "subformulas" that behave as nested implications within the bodies of logic rules. Their inclusion brings the form of rules closer to the less restrictive syntax of first-order logic. These qualities make conditional literals useful tools for knowledge representation. In this paper, we propose a semantics for logic programs with conditional literals and arithmetic based on the SM operator. These semantics do not require grounding, unlike the established semantics for such programs that relies on a translation to infinitary propositional logic. The main result of this paper establishes the precise correspondence between the proposed and existing semantics.
Problem
Research questions and friction points this paper is trying to address.
Defining semantics for logic programs with conditional literals
Developing non-grounding semantics using SM operator
Establishing correspondence between proposed and existing semantics
Innovation
Methods, ideas, or system contributions that make the work stand out.
SM operator semantics for conditional literals
Non-grounding approach to logic programs
Handles arithmetic and conditional constructs
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