Tableaux for Epistemic Gödel Logic

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F25%3A00648124" target="_blank" >RIV/67985807:_____/25:00648124 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/978-3-032-13562-9_17" target="_blank" >https://doi.org/10.1007/978-3-032-13562-9_17</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-032-13562-9_17" target="_blank" >10.1007/978-3-032-13562-9_17</a>

Result language

angličtina

Original language name

Tableaux for Epistemic Gödel Logic

Original language description

We propose a multi-agent epistemic logic capturing reasoning with degrees of plausibility that agents can assign to a given statement with 1 interpreted as ‘entirely plausible for the agent’ and 0 as ‘completely implausible’ (i.e., the agent knows that the statement is false). We formalise such reasoning in an expansion of Gödel fuzzy logic with an involutive negation and multiple S5-like modalities. As already Gödel single-modal logics are known to lack the finite model property w.r.t. their standard [0, 1]-valued Kripke semantics, we provide an alternative semantics that allows for the finite model property. For this semantics, we construct a strongly terminating tableaux calculus that allows us to produce finite counter-models of non-valid formulas. We then use the tableaux to show that the validity problem in our logic is PSpace-complete when there are two or more agents, and coNP-complete for the single-agent case.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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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

Article name in the collection

PRIMA 2025: Principles and Practice of Multi-Agent Systems. Proceedings

ISBN

978-3-032-13561-2

ISSN

0302-9743

e-ISSN

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Number of pages

19

Pages from-to

232-250

Publisher name

Springer

Place of publication

Cham

Event location

Modena

Event date

Dec 16, 2025

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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