相关论文: Well-founded and Stable Semantics of Logic Program…

We study fixpoints of operators on lattices. To this end we introduce the notion of an approximation of an operator. We order approximations by means of a precision ordering. We show that each lattice operator O has a unique most precise or…

We propose a stable model semantics for higher-order logic programs. Our semantics is developed using Approximation Fixpoint Theory (AFT), a powerful formalism that has successfully been used to give meaning to diverse non-monotonic…

This technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion of aggregate solution. Under certain conditions, this operator…

The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well founded semantics corresponds to the…

Answer set programming (ASP) is a logic programming paradigm that can be used to solve complex combinatorial search problems. Aggregates are an ASP construct that plays an important role in many applications. Defining a satisfactory…

We define a novel, extensional, three-valued semantics for higher-order logic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of…

Weight constraint and aggregate programs are among the most widely used logic programs with constraints. In this paper, we relate the semantics of these two classes of programs, namely the stable model semantics for weight constraint…

In [Hitzler and Wendt 2002, 2005], a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the well-founded…

In this note, we use Kunen's notion of a signing to establish two theorems about the well-founded semantics of logic programs, in the case where we are interested in only (say) the positive literals of a predicate $p$ that are consequences…

Logic programs with aggregates (LPA) are one of the major linguistic extensions to Logic Programming (LP). In this work, we propose a generalization of the notions of unfounded set and well-founded semantics for programs with monotone and…

Semantics of logic programs has been given by proof theory, model theory and by fixpoint of the immediate-consequence operator. If clausal logic is a programming language, then it should also have a compositional semantics. Compositional…

We analyze the problem of defining well-founded semantics for ordered logic programs within a general framework based on alternating fixpoint theory. We start by showing that generalizations of existing answer set approaches to preference…

Logic programming has developed as a rich field, built over a logical substratum whose main constituent is a nonclassical form of negation, sometimes coexisting with classical negation. The field has seen the advent of a number of…

The paper presents two equivalent definitions of answer sets for logic programs with aggregates. These definitions build on the notion of unfolding of aggregates, and they are aimed at creating methodologies to translate logic programs with…

This paper shows that the semantics of programs with aggregates implemented by the solvers clingo and dlv can be characterized as extended First-Order formulas with intensional functions in the logic of Here-and-There. Furthermore, this…

An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with…

Logic programming with fixed-point definitions is a useful extension of traditional logic programming. Fixed-point definitions can capture simple model checking problems and closed-world assumptions. Its operational semantics is typically…

Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…

In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…

This paper defines an argumentation semantics for extended logic programming and shows its equivalence to the well-founded semantics with explicit negation. We set up a general framework in which we extensively compare this semantics to…