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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.  ... 

A note on calculi for non-deterministic many-valued logics [article]

Michael Kaminski
2022 arXiv   pre-print
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  
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  
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

Marija Boričić
2019 Bulletin of Symbolic Logic  
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

Walter A. Carnielli, João Marcos
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.  ... 
doi:10.1305/ndjfl/1022615617 dblp:journals/ndjfl/CarnielliM99 fatcat:ria5rmwrifhyvoxquiek63ik2i

Logical calculi for knowledge discovery in databases [chapter]

Jan Rauch
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] .  ... 
doi:10.1007/3-540-63223-9_105 fatcat:xrkrn4hbkzd6jjlh7q2ap3f7ru

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

Urszula Wybraniec-Skardowska
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.  ... 
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?)

Jiří Raclavský
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.  ... 
doi:10.12775/llp.2013.035 fatcat:rznc6umxxnc6taeylyohvgpvwy

Anti-intuitionism and paraconsistency

Andreas B.M. Brunner, Walter A. Carnielli
2005 Journal of Applied Logic  
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]

Sopo Pkhakadze
2019 arXiv   pre-print
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  
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

Marcelo Esteban Coniglio
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] .  ... 
doi:10.1007/s11787-007-0019-6 fatcat:lblyfdgrfvhuncfmwpba2g6d7m

Multi-valued Calculi for Logics Based on Non-determinism

Arnon Avron, Beata Konikowska
2005 Logic Journal of the IGPL  
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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