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Page 13 of Mathematical Reviews Vol. , Issue 80A
[page]

1980
*
Mathematical Reviews
*

Szeged 7 (1935), 222-243; Jbuch 61, 972] has given

*a*method*of*proving weak*deductive**completeness**of*formalizations*of*functionally*complete*2-*valued**propositional**calculi*by imitating, in*the*formalization ... ,*the*informal process*of*evaluating*the*truth-*value**of**a*formula, given*the*truth-*values**of*its*propositional*variables. ...##
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A note on calculi for non-deterministic many-valued logics
[article]

2022
*
arXiv
*
pre-print

We present two

arXiv:2112.07377v2
fatcat:uw2rfrvt6bguxonxxhkkpyo3we
*deductively*equivalent*calculi*for non-deterministic many-*valued*logics.*One*is defined by axioms and*the*other - by rules*of*inference. ...*The*two*calculi*are obtained from*the*truth tables*of**the*logic under consideration in*a*straightforward manner. ... Introduction Non-deterministic many-*valued*logics [1, 2, 3] are*a*generalization*of*"ordinary" many-*valued*logics and, in this*note*, we extend two*of**the*"deterministic"*calculi*introduced in [9] to ...##
###
Page 1234 of Mathematical Reviews Vol. , Issue 81D
[page]

1981
*
Mathematical Reviews
*

It is known that implications weaker than intuitionistic implication
do not satisfy

*deductive**completeness*.*The*author introduces some extensions*of**deductive**completeness*for these weaker systems. ...*A*formula La takes*the**value*“true” in*a*possible world if and only if*a*takes that*value*in every alternative world, “false” other- 81d:03019 wise. It is argued that L, throws some light*on**A*. J. ...##
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Page 1827 of Mathematical Reviews Vol. , Issue 86e
[page]

1986
*
Mathematical Reviews
*

*The*cor- responding

*m*-

*valued*

*propositional*

*calculi*are also considered. G. E. Tseitlin (Kiev) Oberschelp, W. ...

*A*formalization

*of*

*the*No-

*valued*

*propositional*calculus having C as

*the*only primitive functor has been extended previously by

*the*author to formalizations

*of*

*the*No-

*valued*

*propositional*

*calculi*with variable ...

##
###
Probability Sequent Calculi and Entropy Based Nonclassical Logics Classification

2019
*
Bulletin of Symbolic Logic
*

Journal

doi:10.1017/bsl.2019.33
fatcat:eqkpaz3edbb3tm7mtzlzowiwxi
*of*Logic and Computation, vol. 27 (2017), no. 4, pp. 1157-1168. [8] ,*A**note**on*entropy*of*logic. ...*The*models founded*on*Carnap-Popper-Leblance probability semantics are defined for each*of*these*calculi*and accompanied by*the*corresponding soundness and*completeness*results. ... We also obtain several results relating*the*above problems with choice*on*Baire space (choosing*a*path*on**a*given ill-founded tree) and unique choice*on*Baire space (given*a*tree with*a*unique path, produce ...##
###
Limits for Paraconsistent Calculi

1999
*
Notre Dame Journal of Formal Logic
*

*The*case

*of*da Costa's hierarchy

*of*increasingly weaker paraconsistent

*calculi*, known as C n , 1≤ n≤ ω, is carefully studied.

*The*calculus Preprint. ...

*One*just has to check that all axioms (1) to (10) plus (DL) assume only

*the*

*value*1 in any min-valuation, and that (MP) preserves validity. This proves soundness. ...

*The*authors wish to thank Richard Epstein and an anonymous referee for many helpful comments

*on*

*a*previous version

*of*this paper. ...

##
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Logical calculi for knowledge discovery in databases
[chapter]

1997
*
Lecture Notes in Computer Science
*

*A*b s t r

*a*c t . Observational

*calculi*were defined in relation to GUHA method

*of*mechanising hypotheses formation. ... Logical relation among formulae

*of*observational

*calculi*are discussed and some important results concerning

*deduction*rules are shown. ... Observational

*Calculi*and

*Deduction*Rules At first, we indicate

*a*definition

*of*an observational calculus. We will proceed in

*a*very informal way,

*the*formal

*one*is in [2] . ...

##
###
Page 276 of Mathematical Reviews Vol. 47, Issue 2
[page]

1974
*
Mathematical Reviews
*

*The*section

*on*logic contains

*the*

*propositional*calculus and first order logic (both with and without equality) including

*the*Henkin proof

*of*

*the*

*completeness*theorem. ...

*A*

*deductive*system S(

*M*(

*A*))

*of*

*a*machine is constructed in such

*a*way that

*the*set

*of*all theorems

*of*S(

*M*(

*A*)) coincides with

*the*set

*of*all theorems

*of*

*the*system R-S

*of*

*the*predicate calculus. ...

##
###
Foundations for the formalization of metamathematics and axiomatizations of consequence theories

2004
*
Annals of Pure and Applied Logic
*

*The*main part

*of*

*the*paper surveys research

*on*

*the*theory

*of*

*deductive*systems initiated by Tarski, in particular research

*on*(i)

*the*axiomatization

*of*

*the*general notion

*of*consequence operation, (ii) ... There is

*a*short mention

*of*author's research in

*the*ÿeld. ...

*deductive*system theories based

*on*three-

*valued*

*propositional*

*calculi*T L3 T P3 T

*M*3 Tp S, Cn, c, n S, Cn, c, n, t S, Cn, c, n, k,

*a*Ax. ...

##
###
On the interaction of semantics and deduction in Transparent Intensional Logic (Is Tichý's logic a logic?)

2013
*
Logic and Logical Philosophy
*

*The*validity

*of*an argument, composed

*of*

*propositional*constructions, stems from

*the*properties

*of*

*the*constructions. ... Such properties are displayed by

*the*derivation rules

*of*Tichý's system

*of*

*deduction*. ... I owe thanks to Petr Kuchyňka for discussions

*of*

*the*views presented in this paper and also reading and commenting

*on*an early draft. I would also like to thank Jan Štěpán for comments. ...

##
###
Anti-intuitionism and paraconsistency

2005
*
Journal of Applied Logic
*

This paper aims to help to elucidate some questions

doi:10.1016/j.jal.2004.07.016
fatcat:rcpmpiwsknhq5co466i26a7wua
*on**the*duality between*the*intuitionistic and*the*paraconsistent paradigms*of*thought, proposing some new classes*of*anti-intuitionistic*propositional*...*On**the*other hand, by dualizing*the*hierarchy*of**the*paracomplete (or maximal weakly intuitionistic) many-*valued*logics (I n ) n∈ω we show that*the*anti-intuitionistic hierarchy (I n * ) n∈ω obtained from ... Coniglio for helpful remarks and criticisms in*a*previous version*of*this work. ...##
###
Sequent-Type Proof Systems for Three-Valued Default Logic
[article]

2019
*
arXiv
*
pre-print

In my master's thesis, I introduce sequent-type

arXiv:1905.04725v1
fatcat:5slb6vgasbhfdfxf5cm64vqhh4
*calculi*for*a*variant*of*default logic employing \Lukasiewicz's three-*valued*logic as*the*underlying base logic. ...*of*nonmonotonic reasoning by Bonatti and Olivetti, which employ*a*complementary calculus for axiomatising invalid formulas, taking care*of*expressing*the*consistency condition*of*defaults. ...*Note*that*a*three-*valued*interpretation is*a*mapping which assigns to each atomic formula*of*Ł 3*one**of**the*three truth*values*f , u, or t, and this assignment*of*truth*values*is extended to arbitrary ...##
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Page 711 of Mathematical Reviews Vol. 54, Issue 3
[page]

1977
*
Mathematical Reviews
*

Let

*A*be*a**propositional*formula. It is positive if negations do not occur in it.*The*author considers ordinary*propositional**calculi*(OPC). ...*of**the*time complexity (even*of*nondeterministic Turing machines)*of**the*theory*of*<N*, +> is*noted*(*M*. J. Fischer and*M*. O. Rabin, “*The*com- plexity*of*theories*of*addition”, to appear). ...##
###
Recovering a Logic from Its Fragments by Meta-Fibring

2007
*
Logica Universalis
*

*A*general theorem

*of*preservation

*of*

*completeness*by fibring in Log is also obtained. ... We show that, in general, by fibring two or more fragments

*of*

*a*given logic

*the*resulting logic is weaker than

*the*original

*one*, because some meta-properties

*of*

*the*connectives are lost after

*the*combination ... Acknowledgements: This paper is an improved version

*of*

*the*preprint [7] . ...

##
###
Multi-valued Calculi for Logics Based on Non-determinism

2005
*
Logic Journal of the IGPL
*

Definition 2.1

doi:10.1093/jigpal/jzi030
fatcat:v7wp4tfi5rbwhcbk7hhbwyjnam
*A*non-deterministic matrix (Nmatrix) for L is*a*triple*M*= (V, D, O), where V is*a*non-empty set*of*truth*values*, D is*a*non-empty proper subset*of*V (containing its designated*values*), ... Non-deterministic matrices (Nmatrices) are multiple-*valued*structures in which*the**value*assigned by*a*valuation to*a*complex formula can be chosen non-deterministically out*of**a*certain nonempty set*of*... Acknowledgment This research was supported by*THE*ISRAEL SCIENCE FOUNDATION founded by*The*Israel Academy*of*Sciences and Humanities. ...
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