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Intuitionistic Epistemic Logic, Kripke Models and Fitch's Paradox

2011
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Journal of Philosophical Logic
*

The present work is motivated by two questions. (1) What should an

doi:10.1007/s10992-011-9207-1
fatcat:ufapv7ftjzbdhnqgchfmcwdbfe
*intuitionistic**epistemic**logic*look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? ... This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal*logic*. ... The*first*is whether, and to what extent, using the explicit knowledge operator K is useful in*intuitionistic**logic*and reasoning. ...##
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Intuitionistic hybrid logic: Introduction and survey

2011
*
Information and Computation
*

*Intuitionistic*hybrid

*logic*is hybrid modal

*logic*over an

*intuitionistic*

*logic*basis instead of a classical

*logical*basis. ... In this short paper we introduce

*intuitionistic*hybrid

*logic*and we give a survey of work in the area. ... Acknowledgment The author wish to acknowledge the financial support received from The Danish Natural Science Research Council as funding for the project HYLOCORE (Hybrid

*Logic*, Computation, and Reasoning ...

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Implicit and Explicit Stances in Logic

2018
*
Journal of Philosophical Logic
*

We illustrate the contrast for

doi:10.1007/s10992-018-9485-y
fatcat:b67aboyn65esbalttvohwo2vv4
*intuitionistic*and*epistemic**logic*, then take it further to information dynamics, default reasoning, and other areas, to show its wide scope. ... of*logical*systems. ... The modaldynamic game*logic*of [45] formalizes part of the meta-theory of*first*-*order*evaluation games. ...##
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Page 6059 of Mathematical Reviews Vol. , Issue 2001I
[page]

2001
*
Mathematical Reviews
*

Using this reduction, they isolate some decidable fragments of

*first*-*order*temporal*logics*and of two-sorted*first*-*order**logics*where one sort is time. ... The authors are interested in decidability results for fragments of*first*-*order*temporal*logics*. ...##
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Page 778 of Mathematical Reviews Vol. , Issue 2002B
[page]

2002
*
Mathematical Reviews
*

The authors chose Prolog as the implementation language because of its accessibility and close relationship to

*first*-*order**logic*. ... In this article, the author considers cases when the foreground reasoner is a tableau version of*first*-*order**logic*and the background reasoner is a theory of equality. ...##
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Introduction

2009
*
Synthese
*

The

doi:10.1007/s11229-009-9462-7
fatcat:riedp42cc5gqfikjhls5xy2fsm
*First*Workshop on the Philosophy of Information and*Logic*was held at the Philosophy Centre of the University of Oxford on the weekend of the 3rd and 4th of November, 2007. ... Topics ranged from the algebra and topology of quantum information states, to*logics*of information flow in various contexts (a recurring theme being the information flow involved in*logical*reasoning ... Issues involving factual versus procedural information, and statics versus dynamics, are analysed in*order*to reveal what exactly it is that*intuitionistic**logic*and procedural thinking in contemporary ...##
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Curry-Howard-Lambek Correspondence for Intuitionistic Belief
[article]

2020
*
arXiv
*
pre-print

This paper introduces a natural deduction calculus for

arXiv:2006.02417v2
fatcat:j6nx6b623nagdff656nj7e7sq4
*intuitionistic**logic*of belief 𝖨𝖤𝖫^- which is easily turned into a modal λ-calculus giving a computational semantics for deductions in 𝖨𝖤𝖫^- ... The correspondence between deductions and typed terms is then extended to a categorical semantics for identity of proofs in 𝖨𝖤𝖫^- showing the general structure of such a modality for belief in an*intuitionistic*... After discussing a preliminary version of categorical semantics for*intuitionistic*belief during the*Logic*and Philosophy of Science Seminar of University of Florence in May 2019, I had the great opportunity ...##
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The information in intuitionistic logic

2008
*
Synthese
*

Keywords Information ·

doi:10.1007/s11229-008-9408-5
fatcat:c3k6w6pn7rfr7b67piq2paeyv4
*Intuitionistic**logic*·*Epistemic**logic*· Dynamic*logic**Logic*and information, a web of story lines The notion of information is not a standard theme in*logic*, but it really lies ... We discuss connections between*intuitionistic*models and recent protocol models for dynamic-*epistemic**logic*, as well as more general issues that emerge. ...*First*, it is often said that the above means, without further ado, that*intuitionistic**logic*'lies embedded in the*epistemic**logic*S4', which differs from the usual*epistemic**logics*in having positive ...##
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Page 5301 of Mathematical Reviews Vol. , Issue 2000h
[page]

2000
*
Mathematical Reviews
*

Buss’ operator # associates with every

*first*-*order*theory T the (*intuitionistic*) theory #(T) of sentences valid in those Kripke structures whose worlds are classical models of T [see S.R. Buss, Ann. ... Symbolic*Logic*56 (1991), 1496-1499; per bibl.]. The paper under review replies to objections raised against*epistemic*arithmetic. ...##
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Page 6386 of Mathematical Reviews Vol. , Issue 91M
[page]

1991
*
Mathematical Reviews
*

P.] (2-ALLU-I) Semantics of nonclassical

*first*-*order*predicate*logics*. Mathematical*logic*, 105-116, Plenum, New York, 1990. ... This paper can be viewed as a very rich collection of fundamental information on semantics for*first*-*order*modal and superintuition- istic predicate*logics*. ...##
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Epistemic extensions of combined classical and intuitionistic propositional logic

2017
*
Logic Journal of the IGPL
*

Some

doi:10.1093/jigpal/jzx004
fatcat:5rjivdztmzdljfhuc66xfag2gi
*epistemic*laws of*Intuitionistic**Epistemic**Logic*studied by Artemov and Protopopescu [1] are reflected by classical modal principles. ... Finally, we show that a modification of our semantics yields algebraic models for the systems of*Intuitionistic**Epistemic**Logic*introduced in [1]. ... ϕ → Kϕ valid in*Intuitionistic**Epistemic**Logic*[1] . ...##
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Page 3697 of Mathematical Reviews Vol. , Issue 99f
[page]

1999
*
Mathematical Reviews
*

systems of

*first*-*order*arithmetic. ... A common feature of*intuitionistic*systems of*first*-*order*arith- metic is the following: From a proof of any formula of the form Vx dy A(x, y) one can construct an algorithm f such that A(x, fx) holds. ...##
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Page 3568 of Mathematical Reviews Vol. , Issue 2001F
[page]

2001
*
Mathematical Reviews
*

The author is right to stress the fact that the most striking contributions of

*intuitionistic*mathematics are to be found in the field of mathematical analysis rather than in the fields of*logic*and*first*-*order*-arithmetic ... Then he shows that the*first*-*order**logic*(without identity) is semantically complete. (Here, he relies on the known semantical completeness of a certain system.) ...##
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Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer)

2015
*
ACM Transactions on Computational Logic
*

We produce a decidable super-

doi:10.1145/2811263
fatcat:yrx42apqtvcmvcnxypzwarxtqa
*intuitionistic*normal modal*logic*of internalised*intuitionistic*(and thus disjunctive and monotonic) interactive proofs (LIiP) from an existing classical counterpart of classical ... As a side-effect, we offer a short internalised proof of the Disjunction Property of*Intuitionistic**Logic*(originally proved by Goedel). ... Similarly is LIiP a refinement and extension of the propositional fragment of Wijesekera's system of*first*-*order*constructive modal*logic*[Wij90, Section 1.5]. Proof. ...##
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Page 2374 of Mathematical Reviews Vol. , Issue 91E
[page]

1991
*
Mathematical Reviews
*

This should have reminded him of Gédel’s translation of

*intuitionistic**logic*into classical*epistemic**logic*. ... He tries to narrow the gap between classical and*intuitionistic**logic*, using*epistemic*terminology. ...
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