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Possible worlds and many truth values

1978
*
Studia Logica: An International Journal for Symbolic Logic
*

Previous work has established the existence of analogues

doi:10.1007/bf02124804
fatcat:dncyplliwvatbjxjpwvf3akqru
*in*certain*many*-*valued*modal*logics*of certain familiar*systems*of ordinary modal*logic*. ...*value*from a fixed*many*-*valued*truth-functional*logic*. ...*Theorem*1. Any formula α of any*many*-*valued*modal*logic*M determines the same class of frames as*some*formula α * of ordinary modal*logic*K. The proof of*Theorem*1 proceeds as follows. ...##
###
Page 748 of Mathematical Reviews Vol. 58, Issue 2
[page]

1979
*
Mathematical Reviews
*

Skala, Heinz J. 58 #504

*On**many*-*valued**logics*, fuzzy sets, fuzzy*logics*and their applications. Fuzzy Sets and*Systems*1 (1978), no. 2, 129-149. ... This paper gives a survey of*some*aspects of*many*-*valued**logics*and the theory of fuzzy sets. ...##
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Implementing the meta-theory of deductive systems
[chapter]

1992
*
Lecture Notes in Computer Science
*

We illustrate our technique through several examples, the most extensive of which is an interpretation of classical

doi:10.1007/3-540-55602-8_190
fatcat:flv72p7sqzbf5aib4gmcpfelm4
*logic**in*minimal*logic*through a continuation-passing-style*transformation**on*proofs. ... We exhibit a methodology for formulating and verifying metatheorems about deductive*systems**in*the Elf language, an implementation of the LF*Logical*Framework with an operational semantics*in*the spirit ...*In*Section 4 we sketch a more comprehensive example, verifying an interpretation of classical*logic**in*minimal*logic*by way of a continuation-passing-style (CPS)*transformation**on*proofs. ...##
###
Page 190 of Mathematical Reviews Vol. 38, Issue 2
[page]

1969
*
Mathematical Reviews
*

The paper cites previous work

*on*the subject;*some*of the results have been anticipated, but*many*are claimed to be new. H. B. Curry (Amsterdam) Jankov, V. ... Say that a*system*A of functions of k-*valued**logic*(here- after called “*system*”) is complete under EZ if every function of k-*valued**logic*is computable by a*system*of switching networks which corresponds ...##
###
Page 2729 of Mathematical Reviews Vol. , Issue 2004d
[page]

2004
*
Mathematical Reviews
*

There are infinitely

*many**systems*of paraconsistent*logic*;*some*of them are motivated by philosophical reasons, others origi- nate from scientific or technological problems, for instance, from robotics ...*in*the literature.” 2004d:03057 03B53 de Moraes, Lafayette (BR-PCSP-Q; Sao Paulo); Abe, Jair Minoro (BR-PAUL-II; Sao Paulo)*Some*results*on*JaSkowski’s discursive*logic*. ...##
###
Towards the Formalization of Fractional Calculus in Higher-Order Logic
[article]

2015
*
arXiv
*
pre-print

*In*this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus

*in*the HOL Light

*theorem*prover. ...

*In*the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical

*systems*

*in*various fields of science and engineering. ... Earlier formalization was done

*in*the HOL4

*theorem*prover with the main focus

*on*fractional operators for real-

*valued*functions and the verification of fractional order electrical components. ...

##
###
Relating Z and First-Order Logic

2000
*
Formal Aspects of Computing
*

It discusses

doi:10.1007/s001650070029
fatcat:hxq6mgf52jf3ziw2wxn44ffxtu
*some*of the issues which must be addressed*in*creating a proof technology for Z, namely schemas, undefinedness, and what kind of*logic*to use. ... Despite being widely regarded as a gloss*on*first-order*logic*and set theory, Z has not been found to be very supportive of proof. ... Acknowledgements If I have any insight*in*this area, it has been gained*in*discussions with members of the Z Standards panel. ...##
###
Relating Z and first-order logic
[chapter]

1999
*
Lecture Notes in Computer Science
*

It discusses

doi:10.1007/3-540-48118-4_17
fatcat:bvidc45le5hubehrv3ltxwxgva
*some*of the issues which must be addressed*in*creating a proof technology for Z, namely schemas, undefinedness, and what kind of*logic*to use. ... Despite being widely regarded as a gloss*on*first-order*logic*and set theory, Z has not been found to be very supportive of proof. ... Acknowledgements If I have any insight*in*this area, it has been gained*in*discussions with members of the Z Standards panel. ...##
###
Stabilization of Periodic Switched k-Valued Logical Networks

2021
*
IEEE Access
*

PRELIMINARIES This section gives

doi:10.1109/access.2021.3077387
fatcat:eeftrrlg4bc5jjiqgxkllovnwa
*some*necessary preliminaries*on*Cheng product and periodic switched k-*valued**logical*networks, which will be used*in*the following. A. ...*In*Section II, we recall*some*preliminaries*on*Cheng product and problem formulation which will be used*in*later sections. ... The methods, proposed*in*this paper, are based*on*k-*valued**logical*networks, which is a generalization of traditional BNs. ...##
###
Paraconsistentization and many-valued logics
[article]

2020
*
arXiv
*
pre-print

This paper shows how to

arXiv:2004.14881v1
fatcat:rjsi74tcqbelbhl53z3iupsfne
*transform*explosive*many*-*valued**systems*into paraconsistent*logics*. ... We investigate especially the case of three-*valued**systems*showing how paraconsistent three-*valued**logics*can be obtained from them. ... Standard notions and results*on**many*-*valued**logics*can be found*in*[13] , [17] , [11] , [3] and [19] . ...##
###
Formalization of Laplace Transform Using the Multivariable Calculus Theory of HOL-Light
[chapter]

2013
*
Lecture Notes in Computer Science
*

Algebraic techniques based

doi:10.1007/978-3-642-45221-5_50
fatcat:fks2jihksrfalktlbopv5weapy
*on*Laplace*transform*are widely used for solving differential equations and evaluating transfer of signals while analyzing physical aspects of*many*safety-critical*systems*. ...*In*particular, we use integral, differential, transcendental and topological theories of multivariable calculus to formally define Laplace*transform**in*higher-order*logic*and reason about the correctness ... verifying*many*challenging mathematical*theorems*. ...##
###
Quantum view on contextual logic of composite intelligent devices
[article]

2013
*
arXiv
*
pre-print

Based

arXiv:1301.5419v1
fatcat:fyqol4uukngpvpopa6up4iypua
*on*the ideas of quantum theory of open*systems*(QTOS) we propose the consistent approach to study probabilistic*many*-*valued*propositional*logic*of intelligent devices that are composed from separate ...*In*this preliminary communication we consider only the simplest example of such*systems*, namely, four-*valued*probabilistic*logical*device composed of two*logical*subsystems. ...*transformations*, namely*one*can prove that the following*theorem*has place.Theorem 2 : let A is DP*in*composite*system*and G*some**one*-place admissible transformation.Then A = GAG T is decomposable proposition ...##
###
Page 5172 of Mathematical Reviews Vol. , Issue 99h
[page]

1999
*
Mathematical Reviews
*

for

*many*-*valued**logics*. ...*In*this framework, we prove the categorical equivalence between different kinds of structures that have been introduced*in*order to characterize*some**many*-*valued**logics*semantically. ...##
###
On Some Universal Propositional Proof Systems for Many-Valued Logic

2020
*
Mathematical Problems of Computer Science
*

*Some*uniform Hilbert-like propositional proof

*system*is suggested for all versions of

*many*-

*valued*

*logic*to apply them to 3 versions of 3-

*valued*

*logic*, two of which have only

*one*designated

*value*, and the ... last

*one*has two designated

*values*... Acknowledgements This work was supported by the RA MES State Committee of Science,

*in*the frames of the research project № 18T-1B034. ...

##
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The separable axiomatization of the intermediate propositional systems $S_n $ of Gödel

1966
*
Proceedings of the Japan Academy
*

And

doi:10.3792/pja/1195521794
fatcat:ozwblmtnmjamninrs5oywfp4mi
*in*our paper 6 we introduced two kinds of axiomatization for these S. But the separation*theorem*mentioned below does not hold*on*those axiomatized*systems*. Separation*Theorem*. ...*In*[3 GSdel introduced a series of*many*-*valued*propositional*systems*S, which is widely known and is quite frequently made use of when propositional*systems*are treated. ... And we proved*in*[4 and [5 that the separation*theorem*holds*on*LI+ Z.*In*[6 is proved the Lemma 2.. S LI+Z+X++ Y LI+R. ...
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