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Intuitionistic Epistemic Logic, Kripke Models and Fitch's Paradox

Carlo Proietti
2011 Journal of Philosophical Logic  
The present work is motivated by two questions. (1) What should an 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.  ... 
doi:10.1007/s10992-011-9207-1 fatcat:ufapv7ftjzbdhnqgchfmcwdbfe

Intuitionistic hybrid logic: Introduction and survey

Torben Braüner
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  ... 
doi:10.1016/j.ic.2011.10.001 fatcat:rooysswgnfcqhgvido4vwi3qf4

Implicit and Explicit Stances in Logic

Johan van Benthem
2018 Journal of Philosophical Logic  
We illustrate the contrast for 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.  ... 
doi:10.1007/s10992-018-9485-y fatcat:b67aboyn65esbalttvohwo2vv4

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.  ... 

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.  ... 

Introduction

Luciano Floridi, Sebastian Sequoiah-Grayson
2009 Synthese  
The 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  ... 
doi:10.1007/s11229-009-9462-7 fatcat:riedp42cc5gqfikjhls5xy2fsm

Curry-Howard-Lambek Correspondence for Intuitionistic Belief [article]

Cosimo Perini Brogi
2020 arXiv   pre-print
This paper introduces a natural deduction calculus for 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  ... 
arXiv:2006.02417v2 fatcat:j6nx6b623nagdff656nj7e7sq4

The information in intuitionistic logic

Johan van Benthem
2008 Synthese  
Keywords Information · 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  ... 
doi:10.1007/s11229-008-9408-5 fatcat:c3k6w6pn7rfr7b67piq2paeyv4

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.  ... 

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.  ... 

Epistemic extensions of combined classical and intuitionistic propositional logic

Steffen Lewitzka
2017 Logic Journal of the IGPL  
Some 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] .  ... 
doi:10.1093/jigpal/jzx004 fatcat:5rjivdztmzdljfhuc66xfag2gi

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.  ... 

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.)  ... 

Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer)

Simon Kramer
2015 ACM Transactions on Computational Logic  
We produce a decidable super-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.  ... 
doi:10.1145/2811263 fatcat:yrx42apqtvcmvcnxypzwarxtqa

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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