Related papers: On the analysis of set-based fuzzy quantified reas…
The approach described here allows to use the fuzzy Object Based Representation of imprecise and uncertain knowledge. This representation has a great practical interest due to the possibility to realize reasoning on classification with a…
We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a…
One of the main challenges in the area of Neuro-Symbolic AI is to perform logical reasoning in the presence of both neural and symbolic data. This requires combining heterogeneous data sources such as knowledge graphs, neural model…
Legal syllogism is a form of deductive reasoning commonly used by legal professionals to analyze cases. In this paper, we propose legal syllogism prompting (LoT), a simple prompting method to teach large language models (LLMs) for legal…
Syllogistic reasoning is crucial for sound legal decision-making, allowing legal professionals to draw logical conclusions by applying general principles to specific case facts. While large language models (LLMs) can answer legal questions,…
The treatment of complex systems often requires the manipulation of vague, imprecise and uncertain information. Indeed, the human being is competent in handling of such systems in a natural way. Instead of thinking in mathematical terms,…
Syllogistic reasoning is crucial for Natural Language Inference (NLI). This capability is particularly significant in specialized domains such as biomedicine, where it can support automatic evidence interpretation and scientific discovery.…
A presentation is provided of the basic notions and operations of a) the propositional calculus of a variant of fuzzy logic -- canonical fuzzy logic, CFL -- and in a more succinct and introductory way, of b) the theory of fuzzy sets…
Lukasiewicz logic is a "fuzzy" logic in which truth value can be real numbers in the unit interval. There are connectives for min, max, addition and complement (1-x). The "value" of a closed formula in a fuzzy (relational model) is defined…
This paper presents a Prolog-based reasoning module to generate counterfactual explanations given the predictions computed by a black-box classifier. The proposed symbolic reasoning module can also resolve what-if queries using the…
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…
Logical reasoning is a core capability for large language models (LLMs), yet existing benchmarks that rely solely on final-answer accuracy fail to capture the quality of the reasoning process. To address this, we introduce FineLogic, a…
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…
Description logics are knowledge representation languages that have been designed to strike a balance between expressivity and computational tractability. Many different description logics have been developed, and numerous computational…
We define a stable model semantics for fuzzy propositional formulas, which generalizes both fuzzy propositional logic and the stable model semantics of classical propositional formulas. The syntax of the language is the same as the syntax…
We explore a fuzzy modal logic that can formalise probabilistic reasoning about actions and knowledge. In particular, we deal with contexts involving statements about events expressed via modal formulas, e.g., "after doing $a$, the…
New concepts of rough natural number systems are introduced in this research paper from both formal and less formal perspectives. These are used to improve most rough set-theoretical measures in general Rough Set theory (\textsf{RST}) and…
Fuzzy Description Logics (DLs) provide a means for representing vague knowledge about an application domain. In this paper, we study fuzzy extensions of conjunctive queries (CQs) over the DL $\mathcal{SROIQ}$ based on finite chains of…
Fuzzy answer set programming is a declarative framework for representing and reasoning about knowledge in fuzzy environments. However, the unavailability of fuzzy aggregates in disjunctive fuzzy logic programs, DFLP, with fuzzy answer set…
Fuzzy answer set programming (FASP) combines two declarative frameworks, answer set programming and fuzzy logic, in order to model reasoning by default over imprecise information. Several connectives are available to combine different…