About: Modal Logics of Uncertainty with Two-Layer Syntax: A General Completeness Theorem

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Modal logics with two syntactical layers (both governed by classical logic) have been proposed as logics of uncertainty following Hamblin's seminal idea of reading the modal operator P(A) as 'probably A', meaning that the probability of a formula A is bigger than a given threshold. An interesting departure from that (classical) paradigm has been introduced by Hajek with his fuzzy probability logic when, while still keeping classical logic as interpretation of the lower syntactical layer, he proposed to use Lukasiewicz logic in the upper one, so that the truth degree of P(A) could be directly identified with the probability of A. Later, other authors have used the same formalism with different kinds of uncertainty measures and other pairs of logics, allowing for a treatment of uncertainty of vague events (i.e. also changing the logic in the lower layer). The aim of this paper is to provide a general framework for two-layer modal logics that encompasses all the previously studied two-layer modal fuzzy logics, provides a general axiomatization and a semantics of measured Kripke frames, and prove a general completeness theorem. Modal logics with two syntactical layers (both governed by classical logic) have been proposed as logics of uncertainty following Hamblin's seminal idea of reading the modal operator P(A) as 'probably A', meaning that the probability of a formula A is bigger than a given threshold. An interesting departure from that (classical) paradigm has been introduced by Hajek with his fuzzy probability logic when, while still keeping classical logic as interpretation of the lower syntactical layer, he proposed to use Lukasiewicz logic in the upper one, so that the truth degree of P(A) could be directly identified with the probability of A. Later, other authors have used the same formalism with different kinds of uncertainty measures and other pairs of logics, allowing for a treatment of uncertainty of vague events (i.e. also changing the logic in the lower layer). The aim of this paper is to provide a general framework for two-layer modal logics that encompasses all the previously studied two-layer modal fuzzy logics, provides a general axiomatization and a semantics of measured Kripke frames, and prove a general completeness theorem. (en)
Title	Modal Logics of Uncertainty with Two-Layer Syntax: A General Completeness Theorem Modal Logics of Uncertainty with Two-Layer Syntax: A General Completeness Theorem (en)
skos:prefLabel	Modal Logics of Uncertainty with Two-Layer Syntax: A General Completeness Theorem Modal Logics of Uncertainty with Two-Layer Syntax: A General Completeness Theorem (en)
skos:notation	RIV/67985807:_____/14:00431413!RIV15-GA0-67985807
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GAP202/10/1826)
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Cintula, Petr
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav informatiky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	29692
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/14:00431413
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	two-level modal logic; logics of uncertainty; theory of probability; weakly implicative logics; Kripke frames (en)
http://linked.open.../riv/klicoveSlovo	Kripke frames logics of uncertainty two-level modal logic weakly implicative logics theory of probability
http://linked.open...ontrolniKodProRIV	[4099162C01AA]
http://linked.open...v/mistoKonaniAkce	Valparaíso
http://linked.open...i/riv/mistoVydani	Heidelberg
http://linked.open...i/riv/nazevZdroje	Logic, Language, Information, and Computation
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Matematická fuzzy logika v informatice
http://linked.open...UplatneniVysledku	2014
http://linked.open...iv/tvurceVysledku	Cintula, Petr Noguera, Carles
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2014-09-01 (xsd:date)
issn	0302-9743
number of pages	13 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/978-3-662-44145-9_9
http://purl.org/ne...btex#hasPublisher	Springer-Verlag
https://schema.org/isbn	978-3-662-44144-2

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