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Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates…

We provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the…

In logic programming, dynamic scheduling refers to a situation where the selection of the atom in each resolution (computation) step is determined at runtime, as opposed to a fixed selection rule such as the left-to-right one of Prolog.…

It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different "levels", such that the models of the entire program can be…

We introduce SMProbLog, a generalization of the probabilistic logic programming language ProbLog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly…

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…

We study the following problem: given a class of logic programs C, determine the maximum number of stable models of a program from C. We establish the maximum for the class of all logic programs with at most n clauses, and for the class of…

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…

In this paper, a possibilistic disjunctive logic programming approach for modeling uncertain, incomplete and inconsistent information is defined. This approach introduces the use of possibilistic disjunctive clauses which are able to…

Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs,…

In this paper, we study an extension of the stable model semantics for disjunctive logic programs where each true atom in a model is associated with an algebraic expression (in terms of rule labels) that represents its justifications. As in…

Normal forms for logic programs under stable/answer set semantics are introduced. We argue that these forms can simplify the study of program properties, mainly consistency. The first normal form, called the {\em kernel} of the program, is…

The system PL permits the translation of abstract proofs of program correctness into programs in a variety of programming languages. A programming language satisfying certain axioms may be the target of such a translation. The system PL…

We present a static analysis technique for non-termination inference of logic programs. Our framework relies on an extension of the subsumption test, where some specific argument positions can be instantiated while others are generalized.…

This paper treats logic programming with three kinds of negation: default, weak and strict negations. A 3-valued logic model theory is discussed for logic programs with three kinds of negation. The procedure is constructed for negations so…

Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…

The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of…

This article aims to achieve two goals: to show that probability is not the only way of dealing with uncertainty (and even more, that there are kinds of uncertainty which are for principled reasons not addressable with probabilistic means);…

Many metainterpreters found in the logic programming literature are nondeterministic in the sense that the selection of program clauses is not determined. Examples are the familiar "demo" and "vanilla" metainterpreters. For some…