Related papers: Eliminating Unintended Stable Fixpoints for Hybrid…
Approximation fixpoint theory (AFT) provides an algebraic framework for the study of fixpoints of operators on bilattices and has found its applications in characterizing semantics for various classes of logic programs and nonmonotonic…
Approximation Fixpoint Theory (AFT) is a powerful theory covering various semantics of non-monotonic reasoning formalisms in knowledge representation such as Logic Programming and Answer Set Programming. Many semantics of such non-monotonic…
Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as…
Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, i.e.\ operators whose range are sets…
Many modern solvers and program analyzers rely on non-monotone reasoning (e.g. negation-as-failure, speculative updates, backtracking) for which classical monotone fixed-point methods do not apply. The general problem of finding the fixed…
Fuzzy logic programming is an established approach for reasoning under uncertainty. Several semantics from classical, two-valued logic programming have been generalized to the case of fuzzy logic programs. In this paper, we show that two of…
Approximation Fixpoint Theory (AFT) was founded in the early 2000s by Denecker, Marek, and Truszczy\'nski as an abstract algebraic framework to study the semantics of non-monotonic logics. Since its early successes, the potential of AFT as…
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…
DatalogMTL with negation is an extension of Datalog with metric temporal operators enriched with unstratifiable negation. In this paper, we define the stable, well-founded, Kripke-Kleene, and supported model semantics for DatalogMTL with…
The logic of hybrid MKNF (minimal knowledge and negation as failure) is a powerful knowledge representation language that elegantly pairs ASP (answer set programming) with ontologies. Disjunctive rules are a desirable extension to normal…
Aggregates provide a concise way to express complex knowledge. The problem of selecting an appropriate formalisation of aggregates for answer set programming (ASP) remains unsettled. This paper revisits it from the viewpoint of…
Hybrid Knowledge Bases based on Lifschitz's logic of Minimal Knowledge with Negation as Failure are a successful approach to combine the expressivity of Description Logics and Logic Programming in a single language. Their syntax, defined by…
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…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
Combining the closed-world reasoning of answer set programming (ASP) with the open-world reasoning of ontologies broadens the space of applications of reasoners. Disjunctive hybrid MKNF knowledge bases succinctly extend ASP and in some…
Fixpoints are ubiquitous in computer science and when dealing with quantitative semantics and verification one often considers least fixpoints of (higher-dimensional) functions over the non-negative reals. We show how to approximate the…
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…
Abstract Dialectical Frameworks (ADFs) are argumentation frameworks where each node is associated with an acceptance condition. This allows us to model different types of dependencies as supports and attacks. Previous studies provided a…
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…
Hybrid MKNF knowledge bases have been considered one of the dominant approaches to combining open world ontology languages with closed world rule-based languages. Currently, the only known inference methods are based on the approach of…