Related papers: Non-Expansive Fuzzy Coalgebraic Logic
Modal logics for reasoning about the power of coalitions capture the notion of effectivity functions associated with game forms. The main goal of coalition logics is to provide formal tools for modeling the dynamics of a game frame whose…
Lawvere showed that generalised metric spaces are categories enriched over $[0, \infty]$, the quantale of the positive extended reals. The statement of enrichment is a quantitative analogue of being a preorder. Towards seeking a logic for…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
Fuzzy metric spaces, grounded in t-norms and membership functions, have been widely proposed to model uncertainty in machine learning, decision systems, and artificial intelligence. Yet these frameworks treat uncertainty as an external…
We investigate the expressive power of the two main kinds of program logics for complex, non-regular program properties found in the literature: those extending propositional dynamic logic (PDL), and those extending the modal mu-calculus.…
The concept of a fuzzy number is generalized to the case of a finite carrier set of partially ordered elements, more precisely, a lattice, when a membership function also takes values in a partially ordered set (a lattice). Zadeh's…
In this work we propose a formal system for fuzzy algebraic reasoning. The sequent calculus we define is based on two kinds of propositions, capturing equality and existence of terms as members of a fuzzy set. We provide a sound semantics…
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…
We investigate a non-classical version of linear temporal logic whose propositional fragment is G\"odel--Dummett logic (which is well known both as a superintuitionistic logic and a t-norm fuzzy logic). We define the logic using two natural…
Combining symbolic and neural approaches has gained considerable attention in the AI community, as it is often argued that the strengths and weaknesses of these approaches are complementary. One such trend in the literature are weakly…
Within the framework proposed in this paper, we address the issue of extending the certain networks to a fuzzy certain networks in order to cope with a vagueness and limitations of existing models for decision under imprecise and uncertain…
Polyhedral semantics is a recently introduced branch of spatial modal logic, in which modal formulas are interpreted as piecewise linear subsets of an Euclidean space. Polyhedral semantics for the basic modal language has already been well…
The increasing rise in artificial intelligence has made the use of imprecise language in computer programs like ChatGPT more prominent. Fuzzy logic addresses this form of imprecise language by introducing the concept of fuzzy sets, where…
Large Language Models (LLMs) achieve strong performance in analyzing and generating text, yet they struggle with explicit, transparent, and verifiable reasoning over complex texts such as those containing debates. In particular, they lack…
We establish a generic upper bound ExpTime for reasoning with global assumptions (also known as TBoxes) in coalgebraic modal logics. Unlike earlier results of this kind, our bound does not require a tractable set of tableau rules for the…
For each natural number $n$ we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater than $n$ and no strictly ascending chains. The case $n=0$ is the G\"odel-L\"ob…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
Fuzzy logic is an alternate approach for quantifying uncertainty relating to activity duration. The fuzzy version of the backward recursion has been shown to produce results that incorrectly amplify the level of uncertainty. However, the…
Pattern recognition systems implemented using deep neural networks achieve better results than linear models. However, their drawback is the black box property. This property means that one with no experience utilising nonlinear systems may…
Attack trees are important for security, as they help to identify weaknesses and vulnerabilities in a system. Quantitative attack tree analysis supports a number security metrics, which formulate important KPIs such as the shortest, most…