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Page 13 of Mathematical Reviews Vol. , Issue 80A
[page]
1980
Mathematical Reviews
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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. ...
A note on calculi for non-deterministic many-valued logics
[article]
2022
arXiv
pre-print
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We present two 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 ...
arXiv:2112.07377v2
fatcat:uw2rfrvt6bguxonxxhkkpyo3we
Page 1234 of Mathematical Reviews Vol. , Issue 81D
[page]
1981
Mathematical Reviews
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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. ...
Page 1827 of Mathematical Reviews Vol. , Issue 86e
[page]
1986
Mathematical Reviews
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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
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Journal 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 ...
doi:10.1017/bsl.2019.33
fatcat:eqkpaz3edbb3tm7mtzlzowiwxi
Limits for Paraconsistent Calculi
1999
Notre Dame Journal of Formal Logic
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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. ...
doi:10.1305/ndjfl/1022615617
dblp:journals/ndjfl/CarnielliM99
fatcat:ria5rmwrifhyvoxquiek63ik2i
Logical calculi for knowledge discovery in databases
[chapter]
1997
Lecture Notes in Computer Science
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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] . ...
doi:10.1007/3-540-63223-9_105
fatcat:xrkrn4hbkzd6jjlh7q2ap3f7ru
Page 276 of Mathematical Reviews Vol. 47, Issue 2
[page]
1974
Mathematical Reviews
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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
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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. ...
doi:10.1016/j.apal.2003.11.018
fatcat:y7rcxbnvrne6noplrndfpfkxdu
On the interaction of semantics and deduction in Transparent Intensional Logic (Is Tichý's logic a logic?)
2013
Logic and Logical Philosophy
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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. ...
doi:10.12775/llp.2013.035
fatcat:rznc6umxxnc6taeylyohvgpvwy
Anti-intuitionism and paraconsistency
2005
Journal of Applied Logic
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This paper aims to help to elucidate some questions 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. ...
doi:10.1016/j.jal.2004.07.016
fatcat:rcpmpiwsknhq5co466i26a7wua
Sequent-Type Proof Systems for Three-Valued Default Logic
[article]
2019
arXiv
pre-print
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In my master's thesis, I introduce sequent-type 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 ...
arXiv:1905.04725v1
fatcat:5slb6vgasbhfdfxf5cm64vqhh4
Page 711 of Mathematical Reviews Vol. 54, Issue 3
[page]
1977
Mathematical Reviews
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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
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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] . ...
doi:10.1007/s11787-007-0019-6
fatcat:lblyfdgrfvhuncfmwpba2g6d7m
Multi-valued Calculi for Logics Based on Non-determinism
2005
Logic Journal of the IGPL
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Definition 2.1 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. ...
doi:10.1093/jigpal/jzi030
fatcat:v7wp4tfi5rbwhcbk7hhbwyjnam
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