Publication Date: 2012
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.
Publication Date: 2012
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.
Publication Date: 2013
Analysis (14678284)73(3)pp. 419-422
Publication Date: 2014
Mediterranean Journal of Social Sciences (discontinued) (20392117)5(23)pp. 1949-1955
This paper tries to demonstrate how Jacques Derrida deconstructs Hegel's philosophy through detecting an abyss at the hub of the Hegelian system. Derrida's work on Hegel, Glas, which is concerned with Hegel's philosophy, highlights the remarkable resemblance between Hegel's dialectic and Freud's psychoanalysis. Derrida's argument draws a comparison between the Hegelian concept of Aufhebung and Freud's repression. This comparative study aims at showing that no systematic thinking or analysis can release itself from an indigestible and paradoxical element that constitutes the abyss of the systematic or analytical thinking. The first part of the article shows how Derrida, inspired by Kant, thinks of the abyss of the system as the quasi-transcendental that, in a paradoxical way, makes philosophical system both possible and impossible. Concentrating on the concept of repression, the second part delineates similarities of the dialectic and psychoanalysis. In Hegel's view, there is nothing out of cognition; however, Hegel's obsession with Antigone's tragedy reveals that there are dark sides remained outside of the Hegelian system. The last section deals with these remains in Hegel's account of Antigone. Such abyssal points assert that there is a sort of resistance to psychoanalysis, or the process of analysis in general, which deconstruction has always attempted to make us more sensitive to it. © 2014, Mediterranean Center of Social and Educational Research. All rights reserved.
