Topological Semantics of Justification Logic

2008 ◽  
pp. 30-39 ◽  
Author(s):  
Sergei Artemov ◽  
Elena Nogina
Keyword(s):  
Justification Logic ◽  
Topological Semantics

QUANTIFIED MODAL LOGIC ON THE RATIONAL LINE

2014 ◽  
Vol 7 (3) ◽  
pp. 439-454 ◽  
Author(s):  
PHILIP KREMER
Keyword(s):  
Modal Logic ◽  
Real Line ◽  
Topological Spaces ◽  
Topological Semantics ◽  
Cantor Space ◽  
Quantified Modal Logic ◽  
Propositional Modal Logic ◽  
The Family ◽  
Modal Logic S4 ◽  
Rational Line

AbstractIn the topological semantics for propositional modal logic, S4 is known to be complete for the class of all topological spaces, for the rational line, for Cantor space, and for the real line. In the topological semantics for quantified modal logic, QS4 is known to be complete for the class of all topological spaces, and for the family of subspaces of the irrational line. The main result of the current paper is that QS4 is complete, indeed strongly complete, for the rational line.

scholarly journals A Conflict Tolerant Logic of Explicit Evidence

2021 ◽  
Vol 27 (1) ◽  
pp. 124-144
Author(s):  
Thomas Studer
Keyword(s):  
Modal Logic ◽  
Quantum Physics ◽  
Thought Experiment ◽  
The Other ◽  
Justification Logic ◽  
Epistemic Modal ◽  
Epistemic Reasoning ◽  
Basic Properties

Standard epistemic modal logic is unable to adequately deal with the FrauchigerRenner paradox in quantum physics. We introduce a novel justification logic CTJ, in which the paradox can be formalized without leading to an inconsistency. Still CTJ is strong enough to model traditional epistemic reasoning. Our logic tolerates two different pieces of evidence such that one piece justifies a proposition and the other piece justifies the negation of that proposition. However, our logic disallows one piece of evidence to justify both a proposition and its negation. We present syntax and semantics for CTJ and discuss its basic properties. Then we give an example of epistemic reasoning in CTJ that illustrates how the different principles of CTJ interact. We continue with the formalization of the Frauchiger–Renner thought experiment and discuss it in detail. Further, we add a trust axiom to CTJ and again discuss epistemic reasoning and the paradox in this extended setting.

scholarly journals STRONG COMPLETENESS OF MODAL LOGICS OVER 0-DIMENSIONAL METRIC SPACES

2019 ◽  
Vol 13 (3) ◽  
pp. 611-632
Author(s):  
ROBERT GOLDBLATT ◽  
IAN HODKINSON
Keyword(s):  
Metric Spaces ◽  
Deductive System ◽  
Modal Logics ◽  
Topological Semantics ◽  
Strong Completeness

AbstractWe prove strong completeness results for some modal logics with the universal modality, with respect to their topological semantics over 0-dimensional dense-in-themselves metric spaces. We also use failure of compactness to show that, for some languages and spaces, no standard modal deductive system is strongly complete.

Minimal abductive solutions with explicit justification

2020 ◽  
Author(s):  
Rodrigo Medina-Vega ◽  
Francisco HernÁndez-Quiroz ◽  
Fernando R VelÁzquez-Quesada
Keyword(s):  
Justification Logic ◽  
Precise Meaning

Abstract Abductive problems and their solutions are presented by means of justification logic. We introduce additional meta-constructions in order to generate and compare different solutions to the same abductive problem. Our approach has three advantages: (i) it makes structurally explicit the solution to an abductive problem (as it has a syntactic nature); (ii) it gives a precise meaning to the notion of evidence; (iii) it provides clear definitions and procedures for the comparison of solutions that can be adapted to different needs.

Justification Logic with Confidence

Studia Logica ◽  
2019 ◽  
Vol 108 (4) ◽  
pp. 751-778
Author(s):  
Ted Shear ◽  
John Quiggin
Keyword(s):  
Justification Logic
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