About: Implicational (Semilinear) Logics I: A New Hierarchy

Facets (new session)
Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: Implicational (Semilinear) Logics I: A New Hierarchy Goto Sponge NotDistinct Permalink

An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In abstract algebraic logic, the general study of propositional logics is based on the abstraction of the Lindenbaum-Tarski process, one considers the Leibniz relation of indiscernible formulae. It leads to the Leibniz hierarchy; a classification of logics based on generalized equivalences. We perform an analogous abstract study of non-classical logics based on generalized implications. It yields the hierarchy of implicational logics which expands Leibniz hierarchy. The notion of implicational semilinear logic is then naturally introduced as a property of the implication, namely a logic is an implicational semilinear logic iff it has an implication and is complete w.r.t. the matrices where this implication induces a linear order, a property which is satisfied by majority of fuzzy logics. This hierarchy is then restricted to the semilinear case obtaining a classification that encompasses almost all the known examples of fuzzy logics and suggests new directions for research. In abstract algebraic logic, the general study of propositional logics is based on the abstraction of the Lindenbaum-Tarski process, one considers the Leibniz relation of indiscernible formulae. It leads to the Leibniz hierarchy; a classification of logics based on generalized equivalences. We perform an analogous abstract study of non-classical logics based on generalized implications. It yields the hierarchy of implicational logics which expands Leibniz hierarchy. The notion of implicational semilinear logic is then naturally introduced as a property of the implication, namely a logic is an implicational semilinear logic iff it has an implication and is complete w.r.t. the matrices where this implication induces a linear order, a property which is satisfied by majority of fuzzy logics. This hierarchy is then restricted to the semilinear case obtaining a classification that encompasses almost all the known examples of fuzzy logics and suggests new directions for research. (en)
Title	Implicational (Semilinear) Logics I: A New Hierarchy Implicational (Semilinear) Logics I: A New Hierarchy (en)
skos:prefLabel	Implicational (Semilinear) Logics I: A New Hierarchy Implicational (Semilinear) Logics I: A New Hierarchy (en)
skos:notation	RIV/67985807:_____/10:00342136!RIV11-GA0-67985807
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GEICC/08/E018), Z(AV0Z10300504)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Cintula, Petr
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
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	263122
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/10:00342136
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	abstract algebraic logic; hierarchy of implicational logics; implicative logics; Leibniz hierarchy; linearly ordered logical matrices; mathematical fuzzy logic; non-classical logics; semilinear logics (en)
http://linked.open.../riv/klicoveSlovo	mathematical fuzzy logic abstract algebraic logic non-classical logics semilinear logics Leibniz hierarchy hierarchy of implicational logics implicative logics linearly ordered logical matrices
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[7B8C8DF3185E]
http://linked.open...i/riv/nazevZdroje	Archive for Mathematical Logic
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	Logical Models of Reasoning with Vague Information
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	49
http://linked.open...iv/tvurceVysledku	Cintula, Petr Noguera, C.
http://linked.open...ain/vavai/riv/wos	000277246000001
http://linked.open...n/vavai/riv/zamer	Informatika pro informační společnost: modely, algoritmy, aplikace
issn	1432-0665
number of pages	30 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Implicational (Semilinear) Logics I: A New Hierarchy Implicational (Semilinear) Logics I: A New Hierarchy Implicational (Semilinear) Logics I: A New Hierarchy

Faceted Search & Find service v1.16.118 as of Jun 21 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 35 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software