Related papers: A taxonomy for controlling (in)consistency
It is customary to expect from a logical system that it can be algebraizable, in the sense that an algebraic companion of the deductive machinery can always be found. Since the inception of da Costa's paraconsistent calculi $C_n$, algebraic…
This paper proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this paper we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and…
A thorough investigation of the foundations of paraconsistent logics. Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of…
The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a…
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…
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…
We address the problem of measuring inconsistency in declarative process specifications, with an emphasis on linear temporal logic on fixed traces (LTLff). As we will show, existing inconsistency measures for classical logic cannot provide…
The aim of this article is to generalize logics of formal inconsistency ($\textbf{LFI}$s) to systems dealing with the concept of incompatibility, expressed by means of a binary connective. The basic idea is that having two incompatible…
We present a construction of nondeterministic semantics for some deontic logics based on the class of paraconsistent logics known as Logics of Formal Inconsistency (LFIs), for the first time combining swap structures and Kripke models…
In [1], systems of weakening of intuitionistic negation logic called Z_n and CZ_n were developed in the spirit of da Costa's approach(c.f. [2]) by preserving, differently from da Costa, its fundamental properties: antitonicity, inversion…
A survey of paraconsistent logics that are prominent representatives of the different approaches that have been followed to develop paraconsistent logics is provided. The paraconsistent logics that will be discussed are an enrichment of…
Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in…
For a newcomer, paraconsistent logics can be difficult to grasp. Even experts in logic can find the concept of paraconsistency to be suspicious or misguided, if not actually wrong. The problem is that although they usually have much in…
Probabilistic decoding in Large Language Models (LLMs) often yields inconsistent outputs, particularly on complex or long-form questions. Self-Consistency (SC) mitigates this for short-form QA by majority voting over exact strings, whereas…
Modelling complex information systems often entails the need for dealing with scenarios of inconsistency in which several requirements either reinforce or contradict each other. In this kind of scenarios, arising e.g. in knowledge…
This paper concerns the paraconsistent logic LPQ$^{\supset,\mathsf{F}}$ and an application of it in the area of relational database theory. The notions of a relational database, a query applicable to a relational database, and a consistent…
Live sequence charts (LSCs) have been proposed as an inter-object scenario-based specification and visual programming language for reactive systems. In this paper, we introduce a logic-based framework to check the consistency of an LSC…
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…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their…