Related papers: Syntax and semantics of multi-adjoint normal logic…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…
Generalized nonlinear programming is considered without any convexity assumption, capturing a variety of problems that include nonsmooth objectives, combinatorial structures, and set-membership nonlinear constraints. We extend the augmented…
We present alternative definitions of the first-order stable model semantics and its extension to incorporate generalized quantifiers by referring to the familiar notion of a reduct instead of referring to the SM operator in the original…
Some normal logic programs under the answer set (stable model) semantics lack the appealing property of "cautious monotonicity." That is, augmenting a program with one of its consequences may cause it to lose another of its consequences.…
We analyze the problem of defining well-founded semantics for ordered logic programs within a general framework based on alternating fixpoint theory. We start by showing that generalizations of existing answer set approaches to preference…
Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise)…
Common approaches to concurrent programming begin with languages whose semantics are naturally sequential and add new constructs that provide limited access to concurrency, as exemplified by futures. This approach has been quite successful,…
A classical result by Floyd ("On the non-existence of a phrase structure grammar for ALGOL 60", 1962) states that the complete syntax of any sensible programming language cannot be described by the ordinary kind of formal grammars…
Temporal reasoning in dynamic, data-intensive environments increasingly demands expressive yet tractable logical frameworks. Traditional approaches often rely on negation to express absence or contradiction. In such contexts,…
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…
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…
Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…
Belief revision has been studied mainly with respect to background logics that are monotonic in character. In this paper we study belief revision when the underlying logic is non-monotonic instead--an inherently interesting problem that is…
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…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
This paper presents a method of computing a revision of a function-free normal logic program. If an added rule is inconsistent with a program, that is, if it leads to a situation such that no stable model exists for a new program, then…
Rewriting logic is both a flexible semantic framework within which widely different concurrent systems can be naturally specified and a logical framework in which widely different logics can be specified. Maude programs are exactly rewrite…
In this paper we introduce a Conditional Answer Set Programming framework (Conditional ASP) for the definition of conditional extensions of Answer Set Programming (ASP). The approach builds on a conditional logic with typicality, and on the…
The paper introduces fuzzy linguistic logic programming, which is a combination of fuzzy logic programming, introduced by P. Vojtas, and hedge algebras in order to facilitate the representation and reasoning on human knowledge expressed in…