A Tableau Calculus for Equilibrium Entailment

2006

Ann Math Artif Intell

Self Cite

141

108

Section: Tableaux Systemsmentioning

confidence: 99%

Equilibrium logic

2006

Ann Math Artif Intell

Self Cite

141

108

“…As a logical foundation for answer set programming we use the nonclassical logic of here-and-there, denoted here by N 3 , and its nonmonotonic extension, equilibrium logic [18], which generalises answer set semantics for logic programs to arbitrary propositional theories (see eg [14]). We give only a very brief overview here, for more details the reader is referred to [18,14,20] and the logic texts cited below. 4 Given a propositional signature V we define the corresponding propositional language L V as the set of formulas built from atoms in V with the usual connectives , ⊥, ¬, ∧, ∨, →.…”

Section: Equilibrium Logicmentioning

confidence: 99%

“…Answer set semantics was already generalised and extended to arbitrary propositional theories with two negations in the system of equilibrium logic, defined in [18] and further studied in [19][20][21]. Equilibrium logic is based on a simple, minimal model construction in the nonclassical logic of here-and-there (with strong negation), and admits also a natural fixpoint characterisation in the style of nonmonotonic logics.…”

Section: Introductionmentioning

confidence: 99%

Reducing Propositional Theories in Equilibrium Logic to Logic Programs

Cabalar

Progress in Artificial Intelligence

Valverde

2005

Self Cite

Abstract. The paper studies reductions of propositional theories in equilibrium logic to logic programs under answer set semantics. Specifically we are concerned with the question of how to transform an arbitrary set of propositional formulas into an equivalent logic program and what are the complexity constraints on this process. We want the transformed program to be equivalent in a strong sense so that theory parts can be transformed independent of the wider context in which they might be embedded. It was only recently established [2] that propositional theories are indeed equivalent (in a strong sense) to logic programs. Here this result is extended with the following contributions. (i) We show how to effectively obtain an equivalent program starting from an arbitrary theory. (ii) We show that in general there is no polynomial transformation if we require the resulting program to share precisely the vocabulary or signature of the initial theory. (iii) Extending previous work we show how polynomial transformations can be achieved if one allows the resulting program to contain new atoms. The program obtained is still in a strong sense equivalent to the original theory, and the answer sets of the theory can be retrieved from it.

“…We give an overview of the logic here; for more details see [27,22,28] and the logic texts cited. Formulas of N 5 are built-up in the usual way using the logical constants: ∧, ∨, →, ¬, ∼, standing respectively for conjunction, disjunction, implication, weak (or intu- 4 While there are infinitely many logics between intuitionistic and classical logic, there are none at all between here-and-there and classical.…”

Section: Logical Backgroundmentioning

confidence: 99%

“…It was studied in the first-order case by Gurevich [14] and independently in the propositional case by Vakarelov [35] who showed that it is equivalent, via a suitable translation, to Lukasiewicz's 3-valued logic. Tableau calculi for both N 5 and N 3 can be found in [28]. For the logic of here-and-there, ie N 5 without strong negation, a tableau calculus is presented in [1].…”

Section: Logical Backgroundmentioning

confidence: 99%

Simplifying Logic Programs Under Answer Set Semantics

2004

Logic Programming

Self Cite

Abstract. Now that answer set programming has emerged as a practical tool for knowledge representation and declarative problem solving there has recently been a revival of interest in transformation rules that allow for programs to be simplified and perhaps even reduced to programs of 'lower' complexity. Although it has been known for some that there is a maximal monotonic logic, denoted by N5, with the property that its valid (equivalence preserving) inference rules provide valid transformations of programs under answer set semantics, with few exceptions this fact has not really been exploited in the literature. The paper studies some new transformation rules using N5-inference to simplify extended disjunctive logic programs known to be strongly equivalent to programs with nested expressions.