Characterising equilibrium logic and nested logic programs: Reductions and complexity,

Characterising equilibrium logic and nested logic programs: Reductions and complexity,

Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations are permitted in heads and bodies of rules, as special kinds of theories. In this paper, we present polynomial reductions of the main reasoning tasks associ...

Characterising and Explaining Inconsistency in Logic Programs

Possibilistic Nested Logic Programs

We introduce the class of possibilistic nested logic programs. These possibilistic logic programs allow us to use nested expressions in the bodies and the heads of their rules. By considering a possibilistic nested logic program as a possibilistic theory, a construction of a possibilistic logic programing semantics based on answer sets for nested logic programs and the proof theory of possibili...

Nested Epistemic Logic Programs

Nested logic programs and epistemic logic programs are two important extensions of answer set programming. However, the relationship between these two formalisms is rarely explored. In this paper we first introduce the epistemic HT-logic, and then propose a more general extension of logic programs called nested epistemic logic programs. The semantics of this extension named equilibrium views is...

Infinitary equilibrium logic and strongly equivalent logic programs

Strong equivalence is an important concept in the theory of answer set programming. Informally speaking, two sets of rules are strongly equivalent if they have the same meaning in any context. Equilibrium logic was used to prove that sets of rules expressed as propositional formulas are strongly equivalent if and only if they are equivalent in the logic of here-and-there. We extend this line of...