Studies in Logic and the Foundations of MathematicsFitting, M. C. (1969a). "Chapter 1: Propositional Intuitionistic Logic Semantics". In: Intuitionistic Logic Model Theory and Forcing. Vol. 54. Studies in Logic and the Foundations of Mathematics. Elsevier, pp. 19-27. doi: 10.1016/S0049- ...
It is commonly assumed that classical logic is the embodiment of a realist ontology. In his article `Sets and Semantics', however, Jonathan Lear has challenged this assumption in the particular case of set theory, arguing that even if one is a set-theoretic Platonist, due attention to a spe...
Let ZF be the usual Zermelo-Fraenkel set theory formulated without identity, and with the collection axiom scheme. Let ZF-extensionality be obtained from ZF by using intuitionistic logic instead of classical logic, and dropping the axiom of extensionality. We give a syntactic transformation of ZF...
Logic and game theoryEpistemic logicIntuitionistic logicKripke-type semanticsC70Epistemic logic of shallow depths has been developed by Kaneko–Suzuki using classical logic. In this paper, we adopt intuitionistic logic as the base logic to limit each player’s reasoning to constructive one. The ...
set[0,1]Qof rational numbers from the real unit interval, our logic is not compact. In order to obtain a strong complete axiomatization, we introduce an infinitary inference rule with a countable set of premises. The main technical results are the proofs of strong completeness and decidability...
. "Chapter 2: Propositional Intuitionistic Logic Proof Theory". In: Intuition- istic Logic Model Theory and Forcing. Vol. 54. Studies in Logic and the Foundations of Mathematics. Elsevier, pp. 28-37. doi: 10.1016/S0049- 237X(08)70796- 1 (see p. 15)....
Valentini, S. , 'The judgement calculus for intuitionistic linear logic: proof theory and semantics', Zeitschrift f. math. Log. 38,no. 1, 1992, 38-58.S. Valentini. The judgement calculus for intuitionistic linear logic: proof the- ory and semantics. Technical Report 64/89, University of ...
Many influential writers have felt that the open-endedness of the set concept mandates the use of intuitionistic logic in set theory.1But with the exception of Lear, no one has spelt out the implication; it has only been gestured at. Nevertheless, despite its importance and frequent citation...
Rauszer, C.: Model theory for an extension of intuitionistic logic, Studia Logica 36 (1977), 73–87.C. Rauszer, Model theory for an extension of intuitionistic logic, Studia Logica 36 (1977), No. 1-2, pp. 73-87.Rauszer, C. 1977b. Model theory for an extension of intuitionistic ...
Intuitionistic epistemic logicModal type theoryFunctional programmingApplicative functorThe modal intuitionistic epistemic logic was proposed by Artemov and Protopopescu as the intuitionistic version of belief logic. We construct the modal lambda calculus which is Curry-Howard isomorphic to as the type-...