Related papers: Extending Coinductive Logic Programming with Co-Fa…
Extensional higher-order logic programming has been introduced as a generalization of classical logic programming. An important characteristic of this paradigm is that it preserves all the well-known properties of traditional logic…
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…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…
This paper presents a property of propositional theories under the answer sets semantics (called Equilibrium Logic for this general syntax): any theory can always be reexpressed as a strongly equivalent disjunctive logic program, possibly…
We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform, coinductive way. The setup captures rewrite sequences of arbitrary ordinal length, but it has…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…
Negation as failure and incomplete information in logic programs have been studied by many researchers In order to explains HOW a negated conclusion was reached, we introduce and proof a different way for negating facts to overcoming…
Logic programming has developed as a rich field, built over a logical substratum whose main constituent is a nonclassical form of negation, sometimes coexisting with classical negation. The field has seen the advent of a number of…
Rules in logic programming encode information about mutual interdependencies between literals that is not captured by any of the commonly used semantics. This information becomes essential as soon as a program needs to be modified or…
Recent years have witnessed an increasing interest in training machines with reasoning ability, which deeply relies on accurately and clearly presented clue forms. The clues are usually modeled as entity-aware knowledge in existing studies.…
In everyday life it happens that a person has to reason about what other people think and how they behave, in order to achieve his goals. In other words, an individual may be required to adapt his behaviour by reasoning about the others'…
A propositional logic program $P$ may be identified with a $P_fP_f$-coalgebra on the set of atomic propositions in the program. The corresponding $C(P_fP_f)$-coalgebra, where $C(P_fP_f)$ is the cofree comonad on $P_fP_f$, describes…
We introduce DeepProbLog, a probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques can be adapted for the new language. Our experiments…
The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules…
To appear in Theory and Practice of Logic Programming (TPLP). In this paper we propose an extension of logic programming (LP) where each default literal derived from the well-founded model is associated to a justification represented as an…
Program logics are a powerful formal method in the context of program verification. Can we develop a counterpart of program logics in the context of language verification? This paper proposes language logics, which allow for statements of…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
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…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…