Related papers: Fuzzy Logic in Narrow Sense with Hedges
Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for…
Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…
Effective evaluation of large language models (LLMs) remains a critical bottleneck, as conventional direct scoring often yields inconsistent and opaque judgments. In this work, we adapt the Analytic Hierarchy Process (AHP) to LLM-based…
Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1],…
Evaluating argument strength in quantitative argumentation systems has received increasing attention in the field of abstract argumentation. The concept of acceptability degree is widely adopted in gradual semantics, however, it may not be…
A new approach for uncertainty management for fuzzy, rule based decision support systems is proposed: The domain expert's knowledge is expressed by a set of rules that frequently refer to vague and uncertain propositions. The certainty of…
Current high-performance semantic segmentation models are purely data-driven sub-symbolic approaches and blind to the structured nature of the visual world. This is in stark contrast to human cognition which abstracts visual perceptions at…
FASILL (acronym of "Fuzzy Aggregators and Similarity Into a Logic Language") is a fuzzy logic programming language with implicit/explicit truth degree annotations, a great variety of connectives and unification by similarity. FASILL…
Over past several years, deep learning has achieved huge successes in various applications. However, such a data-driven approach is often criticized for lack of interpretability. Recently, we proposed artificial quadratic neural networks…
We propose an integration of possibility theory into non-classical logics. We obtain many formal results that generalize the case where possibility and necessity functions are based on classical logic. We show how useful such an approach is…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
A review is presented of the correspondence existing in both classical bivalent logic (BL) and canonical fuzzy logic (CFL) between each law or tautology in propositional calculus and a law in set theory. The latter law consists of the…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to reveal the dynamical notions inherent in logical computational systems. The fundamental notions of proposition and truth-value in standard logic…
Systems of fuzzy relation equations and inequalities in which an unknown fuzzy relation is on the one side of the equation or inequality are linear systems. They are the most studied ones, and a vast literature on linear systems focuses on…
The combination of higher-order theories and fuzzy logic can be useful in decision-making tasks that involve reasoning across abstract functions and predicates, where exact matches are often rare or unnecessary. Developing efficient…
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed…
We introduce two-dimensional logics based on \L{}ukasiewicz and G\"{o}del logics to formalize paraconsistent fuzzy reasoning. The logics are interpreted on matrices, where the common underlying structure is the bi-lattice (twisted) product…
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…
The paper investigates the properties of a fuzzy logic of typicality. The extension of fuzzy logic with a typicality operator was proposed in recent work to define a fuzzy multipreference semantics for Multilayer Perceptrons, by regarding…