Two-layered logics for probabilities and belief functions over Belnap-Dunn logic

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F25%3A00637267" target="_blank" >RIV/67985807:_____/25:00637267 - isvavai.cz</a>

Alternative codes found

RIV/67985955:_____/25:00637267

Result on the web

<a href="https://doi.org/10.1017/S0960129525000064" target="_blank" >https://doi.org/10.1017/S0960129525000064</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/S0960129525000064" target="_blank" >10.1017/S0960129525000064</a>

Result language

angličtina

Original language name

Two-layered logics for probabilities and belief functions over Belnap-Dunn logic

Original language description

This paper is an extended version of Bílková et al. ((2023b). Logic, Language, Information, and Computation. WoLLIC 2023, Lecture Notes in Computer Science, vol. 13923, Cham, Springer Nature Switzerland, 101-117.). We discuss two-layered logics formalising reasoning with probabilities and belief functions that combine the Łukasiewicz [0, 1]-valued logic with Baaz Δ operator and the Belnap-Dunn logic. We consider two probabilistic logics - PrŁ2Δ (introduced by Bílková et al. 2023d. Annals of Pure and Applied Logic, 103338.) and 4PrŁΔ (from Bílková et al. 2023b. Logic, Language, Information, and Computation. WoLLIC 2023, Lecture Notes in Computer Science, vol. 13923, Cham, Springer Nature Switzerland, 101-117.) - that present two perspectives on the probabilities in the Belnap-Dunn logic. In PrŁ2Δ, every event φ has independent positive and negative measures that denote the likelihoods of φ and -φ, respectively. In 4PrŁΔ, the measures of the events are treated as partitions of the sample into four exhaustive and mutually exclusive parts corresponding to pure belief, pure disbelief, conflict and uncertainty of an agent in φ. In addition to that, we discuss two logics for the paraconsistent reasoning with belief and plausibility functions from Bílková et al. ((2023d). Annals of Pure and Applied Logic, 103338.) - BelŁ2Δ and BelNŁ. Both these logics equip events with two measures (positive and negative) with their main difference being that in BelŁ2Δ, the negative measure of φ is defined as the belief in -φ while in BelNŁ, it is treated independently as the plausibility of -φ.We provide a sound and complete Hilbert-style axiomatisation of 4PrŁΔand establish faithful translations between it and PrŁ2Δ. We also show that the validity problem in all the logics is coNP-complete.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GF22-23022L" target="_blank" >GF22-23022L: Coalition and Epistemic Logic: An Intensional Approach to Groups</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematical Structures in Computer Science

ISSN

0960-1295

e-ISSN

1469-8072

Volume of the periodical

35

Issue of the periodical within the volume

April 2025

Country of publishing house

GB - UNITED KINGDOM

Number of pages

35

Pages from-to

e1

UT code for WoS article

001467324500001

EID of the result in the Scopus database

2-s2.0-105002408352