Related papers: Paraconsistency, resolution and relevance
Dictionaries are inherently circular in nature. A given word is linked to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions in this way, one typically finds that…
We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut-elimination and subformula property. Based on the same design,…
Explainable Artificial Intelligence and Formal Argumentation have received significant attention in recent years. Argumentation-based systems often lack explainability while supporting decision-making processes. Counterfactual and…
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…
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…
The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical…
The paper presents a method for obtaining problems whose conclusions contain disjunctive propositions. These problems constitute a version of inverse problems with a given logical structure. The logical models in the groups of problems…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
F-systems are digraphs that enable to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and Yablo's can be analyzed with that tool to find graph-theoretic patterns. In this paper we present the F-systems…
In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…
Quantum computation represents a computational paradigm whose distinctive attributes confer the ability to devise algorithms with asymptotic performance levels significantly superior to those achievable via classical computation. Recent…
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…
For finite-dimensional linear semigroups which leave a proper cone invariant it is shown that irreducibility with respect to the cone implies the existence of an extremal norm. In case the cone is simplicial a similar statement applies to…
Graph pattern mining methods can extract informative and useful patterns from large-scale graphs and capture underlying principles through the overwhelmed information. Contrast analysis serves as a keystone in various fields and has…
We recently reported evidence that large language models are capable of solving a wide range of text-based analogy problems in a zero-shot manner, indicating the presence of an emergent capacity for analogical reasoning. Two recent…
With distributed computing and mobile applications becoming ever more prevalent, synchronizing diverging replicas of the same data is a common problem. Reconciliation -- bringing two replicas of the same data structure as close as possible…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
We contemplate a higher-level bipolar abstract argumentation for non-elementary arguments such as: X argues against Ys sincerity with the fact that Y has presented his argument to draw a conclusion C, by omitting other facts which would not…
We investigate a series of learning kernel problems with polynomial combinations of base kernels, which will help us solve regression and classification problems. We also perform some numerical experiments of polynomial kernels with…
With distributed computing and mobile applications, synchronizing diverging replicas of data structures is a more and more common problem. We use algebraic methods to reason about filesystem operations, and introduce a simplified definition…