Related papers: The Stable Model Semantics for Higher-Order Logic …
In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (c-atoms). These approaches generalize the fixpoint-based and the level mapping based answer…
Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of…
The well-founded semantics is one of the most widely studied and used semantics of logic programs with negation. In the case of finite propositional programs, it can be computed in polynomial time, more specifically, in O(|At(P)|size(P))…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
Stable Model Semantics and Well Founded Semantics have been shown to be very useful in several applications of non-monotonic reasoning. However, Stable Models presents a high computational complexity, whereas Well Founded Semantics is easy…
In logic programming, negation can be interpreted in various ways. Probably best known is the concept of "negation as failure", where "$\mathit{not}\, p$" is true if we have no evidence for $p$. On the other hand, strong negation requires…
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…
Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…
The rules associated with propositional logic programs and the stable model semantics are not expressive enough to let one write concise programs. This problem is alleviated by introducing some new types of propositional rules. Together…
The definition of stable models for propositional formulas with infinite conjunctions and disjunctions can be used to describe the semantics of answer set programming languages. In this note, we enhance that definition by introducing a…
The Smodels system implements the stable model semantics for normal logic programs. It handles a subclass of programs which contain no function symbols and are domain-restricted but supports extensions including built-in functions as well…
In this paper, a Gaifman-Shapiro-style module architecture is tailored to the case of Smodels programs under the stable model semantics. The composition of Smodels program modules is suitably limited by module conditions which ensure the…
Answer Set Programming (ASP) with stable model semantics has proven highly effective for knowledge representation and reasoning. However, the minimality requirement of stable models can be restrictive for applications requiring exploration…
Answer Set Programming (ASP) is a well-established formalism for nonmonotonic reasoning. An ASP program can have no answer set due to cyclic default negation. In this case, it is not possible to draw any conclusion, even if this is not…
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. These justifications are expressed in terms of causal graphs…
Stable Logic Programming (SLP) is an emergent, alternative style of logic programming: each solution to a problem is represented by a stable model of a deductive database/function-free logic program encoding the problem itself. Several…
Recent large language models (LLMs) have achieved impressive reasoning milestones but continue to struggle with high computational costs, logical inconsistencies, and sharp performance degradation on high-complexity problems. While…
Static analysis by abstract interpretation aims at automatically proving properties of computer programs. To do this, an over-approximation of program semantics, defined as the least fixpoint of a system of semantic equations, must be…
The paper presents a constructive fixpoint semantics for autoepistemic logic (AEL). This fixpoint characterizes a unique but possibly three-valued belief set of an autoepistemic theory. It may be three-valued in the sense that for a…
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…