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Justification Logic
  • Reasoning with Reasons
  • Sergei Artemov, Melvin Fitting
  • Published online:
    25 April 2019
    Print publication:
    02 May 2019
  • Classical logic is concerned, loosely, with the behaviour of truths. Epistemic logic similarly is about the behaviour of known or believed truths. Justification logic is a theory of reasoning that enables the tracking of evidence for statements and therefore provides a logical framework for the reliability of assertions. This book, the first in the area, is a systematic account of the subject, progressing from modal logic through to the establishment of an arithmetic interpretation of intuitionistic logic. The presentation is mathematically rigorous but in a style that will appeal to readers from a wide variety of areas to which the theory applies. These include mathematical logic, artificial intelligence, computer science, philosophical logic and epistemology, linguistics, and game theory.

  • INTUITIONISTIC EPISTEMIC LOGIC

  • SERGEI ARTEMOV, TUDOR PROTOPOPESCU
  • Journal:
    The Review of Symbolic Logic / Volume 9 / Issue 2 / June 2016
    Published online by Cambridge University Press:
    21 March 2016, pp. 266-298
    Print publication:
    June 2016

  • We outline an intuitionistic view of knowledge which maintains the original Brouwer–Heyting–Kolmogorov semantics for intuitionism and is consistent with the well-known approach that intuitionistic knowledge be regarded as the result of verification. We argue that on this view coreflection A → KA is valid and the factivity of knowledge holds in the form KA → ¬¬A ‘known propositions cannot be false’.

    We show that the traditional form of factivity KA → A is a distinctly classical principle which, like tertium non datur A ∨ ¬A, does not hold intuitionistically, but, along with the whole of classical epistemic logic, is intuitionistically valid in its double negation form ¬¬(KA ¬ A).

    Within the intuitionistic epistemic framework the knowability paradox is resolved in a constructive manner. We argue that this paradox is the result of an unwarranted classical reading of constructive principles and as such does not have the consequences for constructive foundations traditionally attributed it.

  • THE LOGIC OF JUSTIFICATION

  • SERGEI ARTEMOV
  • Journal:
    The Review of Symbolic Logic / Volume 1 / Issue 4 / December 2008
    Published online by Cambridge University Press:
    01 December 2008, pp. 477-513
    Print publication:
    December 2008

  • We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a robust system of justifications. This renders a new, evidence-based foundation for epistemic logic. As a case study, we offer a resolution of the Goldman–Kripke ‘Red Barn’ paradox and analyze Russell’s ‘prime minister example’ in Justification Logic. Furthermore, we formalize the well-known Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning.

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