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A Note on Flagg and Friedman's Epistemic and Intuitionistic Formal Systems [article]

Alessandro Provetti, Andrea Zucchellini
2015 arXiv   pre-print
We report our findings on the properties of Flagg and Friedman's translation from Epistemic into Intuitionistic logic, which was proposed as the basis of a comprehensive proof method for the faithfulness  ...  We focus on the propositional case and raise the issue of the admissibility of the translated necessitation rule.  ...  Introduction In their work Epistemic and Intuitionistic Formal Systems (1986), Flagg and Friedman gave a new proof-as an alternative to Goodman's [1] -for the faithfulness of the Gödel translation (  ... 
arXiv:1511.07319v1 fatcat:plkpiykem5f5zpdmoyj5mrqvl4

Page 5301 of Mathematical Reviews Vol. , Issue 2000h [page]

2000 Mathematical Reviews  
The formal system is based on a dependency-relation between formulae oc- currences within a given proof and seems of independent interest.  ...  Epistemic arithmetic thus pro- vides the possibility of expressing constructive, classical and even mixed statements in one single formalism.  ... 

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

Cosimo Perini Brogi
2020 arXiv   pre-print
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  ...  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^-  ...  In particular, I wish to thank Reuben Rowe for an enlightening discussion on the way to Rhossili about the behaviour of the ✷ in my formal system.  ... 
arXiv:2006.02417v2 fatcat:j6nx6b623nagdff656nj7e7sq4

Modality Definition Synthesis for Epistemic Intuitionistic Logic via a Theorem Prover [article]

Paul Tarau
2019 arXiv   pre-print
With help of a candidate definition formula generator, we discover epistemic operators for which axioms and theorems of Artemov and Protopopescu's Intuitionistic Epistemic Logic ( IEL) hold and formulas  ...  Keywords: epistemic intuitionistic logic, propositional intuitionistic logic, Prolog-based theorem provers, automatic synthesis of logic systems, definition formula generation algorithms, embedding of  ...  We thank the anonymous reviewers of the EELP'2019 workshop for their careful reading, constructive suggestions and comments.  ... 
arXiv:1907.11838v2 fatcat:tg5brvwjunhlzn5ge6krxndx34

Page 4730 of Mathematical Reviews Vol. , Issue 87i [page]

1987 Mathematical Reviews  
The author introduces a language and a deductive system for arith- metic, using epistemic logic.  ...  Applying well- known diagonal methods, he obtains some metatheorems on his system. He shows how intuitionistic arithmetic may be translated into epistemic arithmetic.  ... 

Page 3697 of Mathematical Reviews Vol. , Issue 99f [page]

1999 Mathematical Reviews  
He conjec- tures that the formal system in which he proves Markov’s principle has the disjunction property and proves the same for some weaker systems.  ...  Gédel’s translation of intuitionistic propositional logic to modal logic has been extended by S. Shapiro to a translation of Heyting arithmetic into a system of epistemic arithmetic.  ... 

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].  ...  The systems IEL − and IEL of Intuitionistic Epistemic Logic studied in [1] are axiomatized by (INT), (A6), intuitionistic co-reflection ϕ → Kϕ instead of (A7), and, only in case of IEL, additionally  ... 
doi:10.1093/jigpal/jzx004 fatcat:5rjivdztmzdljfhuc66xfag2gi

The information in intuitionistic logic

Johan van Benthem
2008 Synthese  
We discuss connections between intuitionistic models and recent protocol models for dynamic-epistemic logic, as well as more general issues that emerge.  ...  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  ...  the original author(s) and source are credited.  ... 
doi:10.1007/s11229-008-9408-5 fatcat:c3k6w6pn7rfr7b67piq2paeyv4

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.  ...  This gives a working understanding of the contrast, though we stop short of a formal definition, and acknowledge limitations and borderline cases.  ...  We use the word 'stance' here, and not 'system', because we do not identify logic with a family of formal systems.  ... 
doi:10.1007/s10992-018-9485-y fatcat:b67aboyn65esbalttvohwo2vv4

Reasoning about proof and knowledge [article]

Steffen Lewitzka
2018 arXiv   pre-print
Epistemic principles are partially adopted from Intuitionistic Epistemic Logic IEL [Artemov and Protopopescu, Rev. Symb. Log. 2016].  ...  Verification-based intuitionistic knowledge formalized in IEL turns out to be a special case of the kind of knowledge described by our S5-style systems.  ...  We summarize the preceding discussion: Logic EL5 * contains classical epistemic logic KT45 and 'a copy' of intuitionistic epistemic logic IEL.  ... 
arXiv:1709.06672v3 fatcat:yigcacb3hbaada2mahmsonrxwq

Page 6386 of Mathematical Reviews Vol. , Issue 91M [page]

1991 Mathematical Reviews  
Earlier the authors of the present paper suggested a system of plau- sible reasonings of a certain type which are based on formalization of the method of agreements and differences (also called J. S.  ...  Whereas Spohn’s rule is defined in terms of the initial epistemic state and some fea- tures of the final epistemic state, the rule of combination is defined in terms of the initial epistemic state and  ... 

Page 2425 of Mathematical Reviews Vol. , Issue 2000d [page]

2000 Mathematical Reviews  
The author discusses and formally defines many (propositional and probabilistic) auto-epistemic notions and principles.  ...  The author tries to develop rigorously a probabilistic auto- epistemology which enables a system to reason about its own epistemic condition.  ... 

Intuitionistic hybrid logic: Introduction and survey

Torben Braüner
2011 Information and Computation  
In this short paper we introduce intuitionistic hybrid logic and we give a survey of work in the area.  ...  Intuitionistic hybrid logic is hybrid modal logic over an intuitionistic logic basis instead of a classical logical basis.  ...  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

Uniqueness and Logical Disagreement

Frederik J. Andersen, Romanian Academy - Iasi Branch
2020 Logos & Episteme: An International Journal of Epistemology  
After presenting uniqueness and clarifying relevant terms, a novel counterexample to the thesis will be introduced. This counterexample involves logical disagreement .  ...  Several objections to the counterexample are then considered, and it is argued that the best responses to the counterexample all undermine the initial motivation for uniqueness.  ...  old system of logic, they have epistemic reasons for accepting whatever system they favor.  ... 
doi:10.5840/logos-episteme20201111 fatcat:dcxxeqnxqbd75dpo3l2hh5uqxa

Epistemic semantics for classical and intuitionistic logic

John N. Martin
1984 Notre Dame Journal of Formal Logic  
The systems are Kleene's three-valued matrix for the strong connectives, Lukasiewicz's three-valued matrix, supervaluations, and Beth's semantics for intuitionistic logic.  ...  Intuitionism and the strong connectives as Kleene originally interprets them represent varieties of antirealism or epistemic semantics. 1 Intuitionistic semantics is bivalent; an assignment of T represents  ...  The whole enterprise of a formal semantics for intuitionistic logic may at first seem bizarre if not incoherent.  ... 
doi:10.1305/ndjfl/1093870571 fatcat:sqafpjhxjncbfgsl3g7prxpxuy
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