Related papers: Paraconsistent Semantics for Extended Fuzzy Logic …
Current vision-language detection and grounding models predominantly focus on prompts with positive semantics and often struggle to accurately interpret and ground complex expressions containing negative semantics. A key reason for this…
We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract…
The term {\em meta-programming} refers to the ability of writing programs that have other programs as data and exploit their semantics. The aim of this paper is presenting a methodology allowing us to perform a correct termination analysis…
Answering logical queries over incomplete knowledge bases is challenging because: 1) it calls for implicit link prediction, and 2) brute force answering of existential first-order logic queries is exponential in the number of existential…
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…
Negation, a linguistic construct conveying absence, denial, or contradiction, poses significant challenges for multilingual multimodal foundation models. These models excel in tasks like machine translation, text-guided generation, image…
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…
A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
Strong equivalence is a well-studied and important concept in answer set programming (ASP). $\rm LP^{MLN}$ is a probabilistic extension of answer set programs with the weight scheme adapted from Markov Logic. Because of the semantic…
The full power of human language-based communication cannot be realized without negation. All human languages have some form of negation. Despite this, negation remains a challenging phenomenon for current natural language understanding…
The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…
Understanding and solving complex reasoning tasks is vital for addressing the information needs of a user. Although dense neural models learn contextualised embeddings, they still underperform on queries containing negation. To understand…
From an inconsistent database non-trivial arguments may be constructed both for a proposition, and for the contrary of that proposition. Therefore, inconsistency in a logical database causes uncertainty about which conclusions to accept.…
Similarity-based Logic Programming (briefly, SLP ) has been proposed to enhance the LP paradigm with a kind of approximate reasoning which supports flexible information retrieval applications. This approach uses a fuzzy similarity relation…
Logic programs are a powerful approach for solving NP-Hard problems. However, due to their declarative nature, debugging logic programs poses significant challenges. Unlike procedural paradigms, which allow for step-by-step inspection of…
Answer Set Programming (ASP) is a popular framework for modeling combinatorial problems. However, ASP cannot easily be used for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines…
Negation operation is important in intelligent information processing. Different with existing arithmetic negation, an exponential negation is presented in this paper. The new negation can be seen as a kind of geometry negation. Some basic…
We introduce a variant of free logic (i.e., a logic admitting terms with nonexistent referents) that accommodates truth-value gluts as well as gaps. Employing a suitable expansion of the Belnap-Dunn four-valued logic, we specify a…
Abstract interpretation is a well-established technique for performing static analyses of logic programs. However, choosing the abstract domain, widening, fixpoint, etc. that provides the best precision-cost trade-off remains an open…