Related papers: Alternative Characterizations for Strong Equivalen…

Existing semantics for answer-set program updates fall into two categories: either they consider only strong negation in heads of rules, or they primarily rely on default negation in heads of rules and optionally provide support for strong…

Hybrid probabilistic logic programs can represent several scenarios thanks to the expressivity of Logic Programming extended with facts representing discrete and continuous distributions. The semantics for this type of programs is crucial…

The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic…

Hoare logics are proof systems that allow one to formally establish properties of computer programs. Traditional Hoare logics prove properties of individual program executions (such as functional correctness). Hoare logic has been…

Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…

Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…

Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…

Multi-adjoint logic programming is a general framework with interesting features, which involves other positive logic programming frameworks such as monotonic and residuated logic programming, generalized annotated logic programs, fuzzy…

We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations,…

Building on our previous work on hybrid polyadic modal logic we identify modal logic equivalents for Matching Logic, a logic for program specification and verification. This provides a rigorous way to transfer results between the two…

Integrating logic rules with other language features is increasingly sought after for advanced applications that require knowledge-base capabilities. To address this demand, increasingly more languages and extensions for such integration…

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…

Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…

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…

Extended multi-adjoint logic programming arises as an extension of multi-adjoint normal logic programming where constraints and a special type of aggregator operator have been included. The use of this general aggregator operator permits to…

We investigate some well-known (and a few not-so-well-known) many-valued logics that have a small number (3 or 4) of truth values. For some of them we complain that they do not have any \emph{logical} use (despite their perhaps having some…

Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…

Every definite logic program has as its meaning a least Herbrand model with respect to the program-independent ordering "set-inclusion". In the case of normal logic programs there do not exist least models in general. However, according to…

Verifying fine-grained optimistic concurrent programs remains an open problem. Modern program logics provide abstraction mechanisms and compositional reasoning principles to deal with the inherent complexity. However, their use is mostly…

Confluence of a nondeterministic program ensures a functional input-output relation, freeing the programmer from considering the actual scheduling strategy, and allowing optimized and perhaps parallel implementations. The more general…