Related papers: From inconsistency to incompatibility
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…
From an inconsistent database non-trivial arguments may be constructed both for a proposition, and for the contrary of that proposition. Therefore, inconsistency in a logical database causes uncertainty about which conclusions to accept.…
The notion of a non-deterministic logical matrix (where connectives are interpreted as multi-functions) extends the traditional semantics for propositional logics based on logical matrices (where connectives are interpreted as functions).…
In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set 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…
During the first step of practical reasoning, i.e. deliberation, an intelligent agent generates a set of pursuable goals and then selects which of them he commits to achieve. An intelligent agent may in general generate multiple pursuable…
Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic, its constructive variants show that both acts admit…
Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several…
The work presents the brief exposition of the proof (in ZF) of inaccessible cardinals nonexistence. To this end in view there is used the apparatus of subinaccessible cardinals and its basic tools -- reduced formula spectra and matrices and…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…
Multialgebras (or hyperalgebras, or non-deterministic algebras) have been very much studied in Mathematics and in Computer Science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic…
In this article, the hierarchy of LFIs L$_n^k$, Logics of Controlled Consistency (LCC), is introduced. Inspired by da Costa's original C$_n$ systems, this hierarchy can represent different degrees of paraconsistent commitment and different…
Inferring from inconsistency and making decisions are two problems which have always been treated separately by researchers in Artificial Intelligence. Consequently, different models have been proposed for each category. Different…
Linearizability is a commonly accepted notion of correctness for libraries of concurrent algorithms, and recent years have seen a number of proposals of program logics for proving it. Although these logics differ in technical details, they…
The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…
This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…
Conceiving of premises as collected into sets or multisets, instead of sequences, may lead to triviality for classical and intuitionistic logic in general proof theory, where we investigate identity of deductions. Any two deductions with…
The problem of explaining inconsistency-tolerant reasoning in knowledge bases (KBs) is a prominent topic in Artificial Intelligence (AI). While there is some work on this problem, the explanations provided by existing approaches often lack…