On Finite-Valued Bimodal Logics with an Application to Reasoning About Preferences
Result description
In a previous paper by Bou et al., the minimal modal logic over a finite residuated lattice with a necessity operator was characterized under different semantics. In the general context of a residuated lattice, the residual negation is not necessarily involutive, and hence a corresponding possibility operator cannot be introduced by duality. In the first part of this paper we address the problem of extending such a minimal modal logic with a suitable possibility operator. In the second part of the paper, we introduce suitable axiomatic extensions of the resulting bimodal logic and define a logic to reason about fuzzy preferences, generalising to the many-valued case a basic preference modal logic considered by van Benthem et al.
Keywords
Many-valued modal logicNecessity and possibility modal operatorsFinite residuated latticeReasoning about graded preferences
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
On Finite-Valued Bimodal Logics with an Application to Reasoning About Preferences
Original language description
In a previous paper by Bou et al., the minimal modal logic over a finite residuated lattice with a necessity operator was characterized under different semantics. In the general context of a residuated lattice, the residual negation is not necessarily involutive, and hence a corresponding possibility operator cannot be introduced by duality. In the first part of this paper we address the problem of extending such a minimal modal logic with a suitable possibility operator. In the second part of the paper, we introduce suitable axiomatic extensions of the resulting bimodal logic and define a logic to reason about fuzzy preferences, generalising to the many-valued case a basic preference modal logic considered by van Benthem et al.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
GF15-34650L: Modeling vague quantifiers in mathematical fuzzy logic
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Advances in Fuzzy Logic and Technology 2017
ISBN
978-3-319-66826-0
ISSN
2194-5357
e-ISSN
—
Number of pages
13
Pages from-to
505-517
Publisher name
Springer
Place of publication
Cham
Event location
Warsaw
Event date
Sep 11, 2017
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000431389900047
Basic information
Result type
D - Article in proceedings
OECD FORD
Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Year of implementation
2018