Logic Journal of the IGPL (13689894)31(1)pp. 1-38
Temporal justification logic is a new family of temporal logics of knowledge in which the knowledge of agents is modelled using a justification logic. In this paper, we present various temporal justification logics involving both past and future time modalities. We combine Artemov's logic of proofs with linear temporal logic with past, and we also investigate several principles describing the interaction of justification and time. We present two kinds of semantics for our temporal justification logics, one based on interpreted systems and Fitting models and the other based on Mkrtychev models, and further, we establish soundness and completeness. We show that the internalization property holds in some of the temporal justification logics. We further investigate the two well-known epistemic-temporal notions of no forgetting and no learning in the framework of justification logics. Finally, we present temporal justification logics that avoid the logical omniscience problem. © 2021 The Author(s). Published by Oxford University Press. All rights reserved.
Studia Logica (15728730)111(4)pp. 573-613
We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in order to have a Boolean structure on proof terms and equality predicate on terms. Moreover, the completeness theorem and certain generalizations of Stone’s representation theorem are obtained for all proposed algebras. © 2023, Springer Nature B.V.
Annals of Pure and Applied Logic (01680072)168(1)pp. 72-111
Justification logics are modal-like logics that provide a framework for reasoning about justifications. This paper introduces labeled sequent calculi for justification logics, as well as for combined modal-justification logics. Using a method due to Sara Negri, we internalize the Kripke-style semantics of justification and modal-justification logics, known as Fitting models, within the syntax of the sequent calculus to produce labeled sequent calculi. We show that all rules of these systems are invertible and the structural rules (weakening and contraction) and the cut rule are admissible. Soundness and completeness are established as well. The analyticity for some of our labeled sequent calculi are shown by proving that they enjoy the subformula, sublabel and subterm properties. We also present an analytic labeled sequent calculus for S4LPN based on Artemov–Fitting models. © 2016 Elsevier B.V.
Electronic Proceedings in Theoretical Computer Science, EPTCS (20752180)243pp. 59-74
Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal logics. The behavior and interaction of agents in distributed system is often modeled using logics of knowledge and time. In this paper, we sketch some preliminary ideas on how the modal knowledge part of such logics of knowledge and time could be replaced with an appropriate justification logic. © S. Bucheli, M. Ghari & T. Studer.
Logic Journal of the IGPL (13689894)24(5)pp. 743-773
Justification logies provide a framework for reasoning about justifications and evidence. In this article, we study a fuzzy variant of justification logics in which an agent's justification for a belief has certainty degree between 0 and 1. We replace the classical base of justification logics with Hájek's rational Pavelka logic. We introduce fuzzy possible world semantics with crisp accessibility relation and also single world models for our logics. We establish soundness and graded-style completeness for both kinds of semantics. We also introduce extensions with product conjunction. Finally, we offer a solution to a variant of the sorites paradox in our fuzzy justification logics. © The Author 2016.
Theory of Computing Systems (14330490)55(1)pp. 1-40
Justification logics are a family of modal epistemic logics which enables us to reasoning about justifications and evidences. In this paper, we introduce evidence-based multi-agent distributed knowledge logics, called distributed knowledge justification logics. The language of our justification logics contain evidence-based knowledge operators for individual agents and for distributed knowledge, which are interpreted respectively as "t is a justification that agent i accepts for F", and "t is a justification that all agents accept for F if they combine their knowledge and justifications". We study basic properties of our logics and prove the conservativity of distributed knowledge justification logics over multi-agent justification logics. We present Kripke style models, pseudo-Fitting and Fitting models, as well as Mkrtychev models (single world Fitting models) and prove soundness and completeness theorems. We also find a class of Fitting models which satisfies the principle of full communication. Finally, we establish the realization theorem, which states that distributed knowledge justification logics can be embedded into the modal distributed knowledge logics, and vise versa. © 2013 Springer Science+Business Media New York.
Journal of Logic and Computation (0955792X)22(5)pp. 1171-1198
Epistemic logics with justification, S4LP and S4LPN, are combinations of the modal epistemic logic S4 and the Logic of Proofs LP, with some connecting principles. These logics together with the modal knowledge operator □F (F is known), contain infinitely many operators of the form t: F (t is a justification for F), where t is a term. Regarding the Realization Theorem of S4, LP is the justification counterpart of S4, in the sense that, every theorem of S4 can be transformed into a theorem of LP (by replacing all occurrences of by suitable terms), and vise versa. In this article, we first introduce a new cut-free sequent calculus LPLG for LP, and then extend it to obtain a cut-free sequent calculus for S4LP and a cut-free hypersequent calculus for S4LPN. All cut elimination theorems are proved syntactically. Moreover, these sequent systems enjoy a weak subformula property. Then, we show that theorems of S4LP can be realized in LP and theorems of S4LPN can be realized in JS5 (the justification counterpart of modal logic S5). Consequently, we prove that S4LP and S4LPN are conservative extensions of LP. © 2011 The Author. Published by Oxford University Press. All rights reserved.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (03029743)7415pp. 91-108
In this paper, we introduce justification counterparts of distributed knowledge logics. Our justification logics include explicit knowledge operators of the form [[t]] iF and , which are interpreted respectively as "t is a justification that agent i accepts for F", and "t is a justification that all agents implicitly accept for F". We present Kripke style models and prove the completeness theorem. Finally, we give a semantical proof of the realization theorem. © 2012 Springer-Verlag.
