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Page 622 of Mathematical Reviews Vol. , Issue 92b
[page]

1992
*
Mathematical Reviews
*

(Russian)

*Syntactical*and semantic investigations in nonextensional*logics*(Russian), 27-35, ““Nauka’”’, Moscow, 1989. In this paper the terms of assertion and*predication*, motivated by G. ... V. (2-AOS-M) Modal companions of superintuitionistic*logics*: syntax, semantics and*preservation**theorems*. (Russian) Mat. Sb. 180 (1989), no. 10, 1415-1427, 1440; translation in Math. ...##
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Page 712 of Mathematical Reviews Vol. 56, Issue 3
[page]

1978
*
Mathematical Reviews
*

This paper considers two different semantics

*for**intuitionistic**logic*: algebraic models and Kripke models. ... Such a correspondence was given by Fitting*for**intuitionistic*propositional calculus, The result of the paper under review is that Fitting’s construction works in two rather 5231 02*LOGIC*AND FOUNDATIONS ...##
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Page 1236 of Mathematical Reviews Vol. 33, Issue 6
[page]

1967
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Mathematical Reviews
*

Then the

*preservation**theorem**for*the given situation says that the senterice F is*preserved*under R if and only if F is*logically*equivalent to some sentence in £. ... Symbolic*Logic*30 (1965), 339-349. In this paper the author proves new*preservation**theorems*. ...##
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Forcing in Proof Theory

2004
*
Bulletin of Symbolic Logic
*

AbstractPaul Cohen's method of forcing, together with Saul Kripke's related semantics

doi:10.2178/bsl/1102022660
fatcat:7sr63xqpabcqjdsuazxbi3rude
*for*modal and*intuitionistic**logic*, has had profound effects on a number of branches of mathematical*logic*, from set ... The latter include ways of obtaining conservation results*for*classical and*intuitionistic*theories, interpreting classical theories in constructive ones, and constructivizing model-theoretic arguments ... . • (monotonicity): p ϕ and q ≤ p imply q ϕ • M ϕ implies ϕ*For**intuitionistic**logic*, add • p ⊥*Theorem*. • p ⊥ → ϕ • I ϕ implies ϕ. 7 Forcing*for*classical*logic*Weak forcing: define C ϕ by M ϕ N . ...##
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Page 25 of Mathematical Reviews Vol. , Issue 91A
[page]

1991
*
Mathematical Reviews
*

Michele (I-BAR])
A comparison between Lambek

*syntactic*calculus and*intuitionistic*linear propositional*logic*. Z. Math. Logik Grundlag. Math. 36 (1990), no. 1, 11-15. ... A formula G is said to be*logically*valid if the truth value 7(G) = 1*for*any interpretation /. The authors prove that the axioms and*theorems*in the system FL are*logically*valid. ...##
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Page 2811 of Mathematical Reviews Vol. , Issue 82g
[page]

1982
*
Mathematical Reviews
*

The author raises three problems: (1) Is every

*logic*with a recursive set of*theorems**syntactically*decidable? (2) Does every*syntactically*decidable S belong to S, or $,? ...*Logic*20 (1981), no. 1, 1-41. 03G Algebraic*logic*82¢:03 107 Most of this paper is devoted to an investigation of familiar concepts of general topology in the context of a higher-order*intuitionistic**logic*...##
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JSL volume 56 issue 2 Cover and Front matter

1991
*
Journal of Symbolic Logic (JSL)
*

GOODE
624
A direct proof of the Feferman-Vaught

doi:10.1017/s0022481200024427
fatcat:rgjbnovj7bdb7k4dx4byxw365i
*theorem*and other*preservation**theorems*in products. ... By KAI HAUSER . . . 439 A generalization of Specker's*theorem*on typical ambiguity. By RICHARD KAYE 458 The*logic*of first order*intuitionistic*type theory with weak sigma-ehmination. By M. ...##
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Full Lambek Hyperdoctrine: Categorical Semantics for First-Order Substructural Logics
[chapter]

2013
*
Lecture Notes in Computer Science
*

different sorts of

doi:10.1007/978-3-642-39992-3_19
fatcat:im6sor55g5ftpcvut3yb2cch2e
*logical*systems (classical,*intuitionistic*, linear, fuzzy, relevant, etc.). ... We pursue the idea that*predicate**logic*is a "fibred algebra" while propositional*logic*is a single algebra; in the context of intuitionism, this algebraic understanding of*predicate**logic*goes back to ... The cut rule*preserves*satisfaction, since tensoring*preserves*≤ and ≤ has transitivity. It is easy to verify that all the rules*for*the*logical*connectives*preserve*satisfaction. ...##
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Page 4589 of Mathematical Reviews Vol. , Issue 82k
[page]

1982
*
Mathematical Reviews
*

This monograph deals with a fully dual

*intuitionistic**predicate**logic*; as such it is a continuation of the author’s earlier papers [see, e.g., Fund. Math. 83 (1973/74), no. 3, 219-249; MR 49 #4763]. ... The properties of semi-Boolean algebras are developed*for*the proof of the completeness*theorem*, in particular the analogue of the Rasiowa-Sikorski lemma on homomorphism-*preserving*denumerable joins and ...##
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Formalizing Cut Elimination of Coalgebraic Logics in Coq
[chapter]

2013
*
Lecture Notes in Computer Science
*

The work presented here can be used to verify cut elimination

doi:10.1007/978-3-642-40537-2_22
fatcat:physiyzxlzbdhp76d2ptoil4xi
*theorems**for*different modal*logics*with considerably less effort in the future. ... In their work on coalgebraic*logics*, Pattinson and Schröder prove soundness, completeness and cut elimination in a generic sequent calculus*for*propositional multi-modal*logics*[1]. ... The*theorem*is proved with the*theorem**syntactic*admissible cut and suitable lemmas*for*the absorption properties of K. ...##
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Page 7660 of Mathematical Reviews Vol. , Issue 2001K
[page]

2001
*
Mathematical Reviews
*

In this paper, we take a type-theoretic view of this approach

*for*the case in which the non-classical*logic*is*intuitionistic*. ... ISBN 968-36-7540-9 This little book is a monograph on the*theorem*of compactness in first-order*logic*and its relation to the*theorem*of complete- ness. ...##
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Intuitionistic Existential Instantiation and Epsilon Symbol
[article]

2012
*
arXiv
*
pre-print

A natural deduction system

arXiv:1208.0861v1
fatcat:5fclulw7gzh53cg7grhbf36zl4
*for**intuitionistic**predicate**logic*with existential instantiation rule presented here uses Hilbert's -symbol. It is conservative over*intuitionistic**predicate**logic*. ... Our system extends*intuitionistic*systems with -symbol due to A. Dragalin and Sh. Maehara. ... Before applying the construction from [1] , let us recall a refinement of a completeness*theorem**for**intuitionistic**predicate**logic*IPC. ...##
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Page 1133 of Mathematical Reviews Vol. , Issue 87c
[page]

1987
*
Mathematical Reviews
*

Andrews)
Doden, Kosta (YU-BELG) 87c:03015 A completeness

*theorem**for*the Lambek calculus of*syntactic*categories. Z. Math. Logik Grundlag. Math. 31 (1985), no. 3, 235-241. In the fifties, J. ... be the*intuitionistic*and the negationless*intuitionistic*propositional*logic*with modus ponens as the sole rule of inference, respectively. It is well known that I and I? ...##
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Affine logic for constructive mathematics
[article]

2021
*
arXiv
*
pre-print

We show that numerous distinctive concepts of constructive mathematics arise automatically from an "antithesis" translation of affine

arXiv:1805.07518v2
fatcat:t34if2wdzreqvecu7mahhzodj4
*logic*into*intuitionistic**logic*via a Chu/Dialectica construction. ... Affine*logic*and the antithesis construction thus systematically "constructivize" classical definitions, handling the resulting bookkeeping automatically. ... classical*theorems*into*intuitionistic*ones; or the Girard translation, which constructs a model of*intuitionistic**logic*from a model of linear*logic*, and therefore transforms*intuitionistic**theorems*...##
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Truthful Monadic Abstractions
[chapter]

2012
*
Lecture Notes in Computer Science
*

In this paper we characterize a family of truth-

doi:10.1007/978-3-642-31365-3_10
fatcat:cg5tck6ydnbjzpzx645sjmvhvq
*preserving*abstractions from*intuitionistic*first-order*logic*to the monadic fragment of classical first-order*logic*. ... Because they are truthful, these abstractions can be used to disprove sequents in*intuitionistic*first-order*logic*. ... Base*logic*:*Intuitionistic*first-order*logic*2. Intermediate*logic*1:*Intuitionistic*first-order*logic*with monadic*predicates*3. Intermediate*logic*2: Monadic*intuitionistic*first-order*logic*4. ...
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