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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.  ...

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  ...

Page 1236 of Mathematical Reviews Vol. 33, Issue 6 [page]

1967 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.  ...

Forcing in Proof Theory

2004 Bulletin of Symbolic Logic
AbstractPaul Cohen's method of forcing, together with Saul Kripke's related semantics 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 .  ...

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.  ...

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  ...

JSL volume 56 issue 2 Cover and Front matter

1991 Journal of Symbolic Logic (JSL)
GOODE 624 A direct proof of the Feferman-Vaught 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.  ...

Full Lambek Hyperdoctrine: Categorical Semantics for First-Order Substructural Logics [chapter]

Yoshihiro Maruyama
2013 Lecture Notes in Computer Science
different sorts of 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.  ...

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  ...

Formalizing Cut Elimination of Coalgebraic Logics in Coq [chapter]

Hendrik Tews
2013 Lecture Notes in Computer Science
The work presented here can be used to verify cut elimination 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.  ...

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.  ...

Intuitionistic Existential Instantiation and Epsilon Symbol [article]

Grigori Mints
2012 arXiv   pre-print
A natural deduction system 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.  ...

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?  ...

Affine logic for constructive mathematics [article]

Michael Shulman
2021 arXiv   pre-print
We show that numerous distinctive concepts of constructive mathematics arise automatically from an "antithesis" translation of affine 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  ...