Abstract
AbstarctIn the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of here-and-there allows us to establish strong equivalence by deriving rules of each group from rules of the other. In the process, rules are rewritten as propositional formulas. We extend this method of proving strong equivalence to an answer set programming language that includes operations on integers. The formula representing a rule in this language is a first-order formula that may contain comparison symbols among its predicate constants, and symbols for arithmetic operations among its function constants. The paper is under consideration for acceptance in TPLP.
Highlights
In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context
Rules are rewritten as propositional formulas
The head and the body of a rule become the consequent and the antecedent of an implication; negationas-failure is replaced by classical negation; and choice expressions are tranformed into excluded middle formulas
Summary
In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The study of strong equivalence for fragments of the input language of gringo may be useful for the practice of answer set programming, because it can help the programmer to see which modifications of a rule or a group of rules preserve the set of stable models. This is important, in particular, because some features of the strong equivalence relation between gringo programs may seem counterintuitive. The paper (Lifschitz et al 2019) where this definition was proposed aimed at verifying strong equivalence of mini-gringo programs using theorem provers for classical logic. We show a pair of strongly equivalent mini-gringo programs to which the method proposed in this paper is not applicable (Section 6) and outline directions for future work (Section 7)
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