Related papers: A note on the Declarative reading(s) of Logic Prog…

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…

We investigate mca-programs, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a non-negative integer and X is a finite set of propositional atoms. We develop a theory of mca-programs. We…

The article demonstrates that logic is not necessarily singleton and does not always have the standard interpretation of negation. Appropriate generalizations of logic are suggested. Positive logic and multivalued negation operations are…

The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…

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…

We develop an extensional semantics for higher-order logic programs with negation, generalizing the technique that was introduced in [Bezem99,Bezem01] for positive higher-order programs. In this way we provide an alternative extensional…

We consider the problem of implementing deontic modal logic. We show how (deontic) modal operators can be elegantly and directly expressed using default negation (negation-as-failure) and strong negation present in answer set programming…

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…

Termination of logic programs depends critically on the selection rule, i.e. the rule that determines which atom is selected in each resolution step. In this article, we classify programs (and queries) according to the selection rules for…

Constraint Logic Programming (CLP) is a logic programming formalism used to solve problems requiring the consideration of constraints, like resource allocation and automated planning and scheduling. It has previously been extended in…

Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms,…

In inductive learning of a broad concept, an algorithm should be able to distinguish concept examples from exceptions and noisy data. An approach through recursively finding patterns in exceptions turns out to correspond to the problem of…

The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the…

Scientists form hypotheses and experimentally test them. If a hypothesis fails (is refuted), scientists try to explain the failure to eliminate other hypotheses. The more precise the failure analysis the more hypotheses can be eliminated.…

The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…

We present a novel approach for teaching logic and the metatheory of logic to students who have some experience with functional programming. We define concepts in logic as a series of functional programs in the language of the proof…

With the technology of the time, Kowalski's seminal 1974 paper {\em Predicate Logic as a Programming Language} was a breakthrough for the use of logic in computer science. It introduced two fundamental ideas: on the declarative side, the…

Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…

Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…