Related papers: A survey of paraconsistent logics
We aim at improving reasoning on inconsistent and uncertain data. We focus on knowledge-graph data, extended with time intervals to specify their validity, as regularly found in historical sciences. We propose principles on semantics for…
We explore the theory of illfounded and cyclic proofs for the propositional modal $\mu$-calculus. A fine analysis of provability for classical and intuitionistic modal logic provides a novel bridge between finitary, cyclic and illfounded…
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results,…
Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary…
With the increasing capabilities of Large Language Models (LLMs), parallel reasoning has emerged as a new inference paradigm that enhances reasoning robustness by concurrently exploring multiple lines of thought before converging on a final…
In this paper we make a contribution to the unification of formal models of defeasible reasoning. We present several translations between formal argumentation frameworks and nonmonotonic logics for reasoning with plausible assumptions. More…
We present a logic for reasoning with if-then formulas which involve constants for rational truth degrees from the unit interval. We introduce graded semantic and syntactic entailment of formulas. We prove the logic is complete in Pavelka…
Large Language Models (LLMs) have grown increasingly powerful, yet ensuring their decisions remain transparent and trustworthy requires self-consistency -- no contradictions in their internal reasoning. Our study reveals that even on simple…
In order to develop efficient tools for automated reasoning with inconsistency (theorem provers), eventually making Logics of Formal inconsistency (LFI) a more appealing formalism for reasoning under uncertainty, it is important to develop…
As of this date of this version, this monograph (part I and II) contains most of the technical results relative to the Robinson-styled nonstandard modeling of natural languages and certain associated linguistic processes such as deduction…
We design an expansion of Belnap--Dunn logic with belief and plausibility functions that allow non-trivial reasoning with inconsistent and incomplete probabilistic information. We also formalise reasoning with non-standard probabilities and…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be…
We study properties related to relevance in non-monotonic consequence relations obtained by systems of structured argumentation. Relevance desiderata concern the robustness of a consequence relation under the addition of irrelevant…
We present a novel approach to querying classical inconsistent description logic (DL) knowledge bases by adopting a~paraconsistent semantics with the four Belnapian values: exactly true ($\mathbf{T}$), exactly false ($\mathbf{F}$), both…
We present a novel treatment of set theory in a four-valued paraconsistent and paracomplete logic, i.e., a logic in which propositions can be both true and false, and neither true nor false. Our approach is a significant departure from…
Computability logic is a formal theory of computability. The earlier article "Introduction to cirquent calculus and abstract resource semantics" by Japaridze proved soundness and completeness for the basic fragment CL5 of computability…
The study of the theory of operators over modal pseudocomplemented De Morgan algebras was begun in the papers [15] and [16]. In this paper, we introduce and study the class of modal pseudocomplemented De Morgan algebras enriched by an…
Large language models (LLMs) and theorem provers (TPs) can be effectively combined for verifiable natural language inference (NLI). However, existing approaches rely on a fixed logical formalism, a feature that limits robustness and…
Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in English natural language. While the progress is promising, it is currently unclear if these models…