Related papers: Fuzzy Answer Set Computation via Satisfiability Mo…
We introduce a two-sort weighted modal logic for possibilistic reasoning with fuzzy formal contexts. The syntax of the logic includes two types of weighted modal operators corresponding to classical necessity ($\Box$) and sufficiency…
This paper presents a tableau calculus for finding a model for a set-satisfiable finite set of formulas of an extended fuzzy logic BL, a fuzzy logic BL with additional Baaz connective and the involutive negation, if such a model exists. The…
In dealing with veracity of data analytics, fuzzy methods are more and more relying on probabilistic and statistical techniques to underpin their applicability. Conversely, standard statistical models usually disregard to take into account…
Answer Set Programming (ASP) is a logic-based knowledge representation framework, supporting---among other reasoning modes---the central task of query answering. In the propositional case, query answering amounts to computing cautious…
Answer Set Programming (ASP) is a well-established formalism for nonmonotonic reasoning. An ASP program can have no answer set due to cyclic default negation. In this case, it is not possible to draw any conclusion, even if this is not…
Answer set programming - the most popular problem solving paradigm based on logic programs - has been recently extended to support uninterpreted function symbols. All of these approaches have some limitation. In this paper we propose a…
In this paper we propose an extension of Answer Set Programming (ASP), and in particular, of its most general logical counterpart, Quantified Equilibrium Logic (QEL), to deal with partial functions. Although the treatment of equality in QEL…
To appear in Theory and Practice of Logic Programming (TPLP) Bound Founded Answer Set Programming (BFASP) is an extension of Answer Set Programming (ASP) that extends stable model semantics to numeric variables. While the theory of BFASP is…
Answer Set Programming (ASP) is a well-known declarative formalism in logic programming. Efficient implementations made it possible to apply ASP in many scenarios, ranging from deductive databases applications to the solution of hard…
Answer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic logic programs. HEX-programs extend ASP with external atoms for accessing arbitrary external information, which can introduce values that do not…
Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable…
With the rapid advancement of large language models (LLMs), natural language processing (NLP) has achieved remarkable progress. Nonetheless, significant challenges remain in handling texts with ambiguity, polysemy, or uncertainty. We…
Fuzzy logic extends the classical truth values "true" and "false" with additional truth degrees in between. More specifically, fuzzy modal logics in this sense are given by a choice of fuzzy modalities and a fuzzy propositional base. It has…
Semantic understanding of programs has attracted great attention in the community. Inspired by recent successes of large language models (LLMs) in natural language understanding, tremendous progress has been made by treating programming…
We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets…
Prediction sets offer a binary inclusion/exclusion for each element at the same fixed confidence level. We generalize to fuzzy prediction sets, which exclude elements at their own data-driven confidence level. Our key insight is that a…
For widespread deployment in domains characterized by partial observability, non-deterministic actions and unforeseen changes, robots need to adapt sensing, processing and interaction with humans to the tasks at hand. While robots typically…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
Most fuzzy systems including fuzzy decision support and fuzzy control systems provide out-puts in the form of fuzzy sets that represent the inferred conclusions. Linguistic interpretation of such outputs often involves the use of linguistic…
It is worth noticing that a fuzzy conjunction and its corresponding fuzzy implication can form a residual pair if and only if it is left-continuous. In order to get a more general result related on residual implications that induced by…