A new epistemic model

Meier (2012) gave a "mathematical logic foundation" of the purely measurable universal type space (Heifetz and Samet, 1998). The mathematical logic foundation, however, discloses an inconsistency in the type space literature: a finitary language is used for the belief hierarchies and an infinitary language is used for the beliefs. In this paper we propose an epistemic model to fix the inconsistency above. We show that in this new model the universal knowledgebelief space exists, is complete and encompasses all belief hierarchies. Moreover, by examples we demonstrate that in this model the players can agree to disagree Aumann (1976)'s result does not hold, and Aumann and Brandenburger (1995)'s conditions are not sufficient for Nash equilibrium. However, we show that if we substitute selfevidence (Osborne and Rubinstein, 1994) for common knowledge, then we get at that both Aumann (1976)'s and Aumann and Brandenburger (1995)'s results hold.

Remarks on mathematical or demonstrative reasoning; its connexion with logic; and its application to science, physical and metaphysical, with reference to some recent publications.

Mode of access: Internet.

An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities.

Mode of access: Internet.

An investigation of the laws of thought, on which are founded mathematical theories of logic and probabilities.

Mode of access: Internet.

A Mathematical Apparatus for Domain Ontology Simulation. An Extendable Language of Applied Logic

* This paper was made according to the program of fundamental scientific research of the Presidium of the Russian Academy of Sciences «Mathematical simulation and intellectual systems», the project "Theoretical foundation of the intellectual systems based on ontologies for intellectual support of scientific researches".

A Mathematical Apparatus for Ontology Simulation. Specialized Extensions of the Extendable Language of Applied Logic

* This paper was made according to the program of fundamental scientific research of the Presidium of the Russian Academy of Sciences «Mathematical simulation and intellectual systems», the project "Theoretical foundation of the intellectual systems based on ontologies for intellectual support of scientific researches".

A logic-mathematical point of view of the truth: Reality, perception, and language

In this article, the authors propose a theory of the truth value of propositions from a logic-mathematical point of view. The work that the authors present is an attempt to address this question from an epistemological, linguistic, and logical-mathematical point of view. What is it to exist and how do we define existence? The main objective of this work is an approach to the first of these questions. We leave a more thorough treatment of the problem of existence for future works.