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Many-worlds theory of truth
author: Alexander Boldachev,
The logical world is a set of propositions, united by common principles of establishing their truth. The many-worlds theory asserting that the truth of any proposition in any given logical world is always established by comparing it with standard propositions in this world – directly or via the procedure of transferring the truth.


Preface. Conditional:
Conceptual and Historical Analysis

author: Fabien Schang,
The logic of conditional is developed hereby in a series of papers, contributing to a historical and critical analysis of what the logical constant is expected to mean.

The Semantics and Pragmatics of the Conditional
in al-Fārābī’s and Avicenna’s Theories

author: Saloua Chatti,
In this paper, I examine al-Fārābī's and Avicenna's conceptions of the conditional. I show that there are significant differences between the two frames, despite their closeness. Al-Fārābī distinguishes between an accidental conditional and two “essential” conditionals. The accidental conditional can occur only once and pragmatically involves succession. In the first “essential” conditional, the consequent follows regularly the antecedent; pragmatically it involves likeliness. The second “essential” conditional can be either complete or incomplete. Semantically the former means “if and only if”; pragmatically it means “necessarily if and only if”. The latter is expressed by ‘if, then’ and means entailment; pragmatically, it involves necessity and the inclusion of the antecedent into the consequent. As to Avicenna, he rejects explicitly al-Fārābī’s complete conditional and distinguishes between the luzūm (real implication) and what he calls ittifāq. He quantifies over situations (or times) to express the various conditionals. The two universals AC and EC are expressed by “In all situations, if…, then…”, while the two particulars IC and OC are expressed by “In some situations, if…, then..”. This gives them a modal connotation, and makes the universals close to strict implications. Pragmatically, AC presupposes the truth of the antecedent, but there is no such presupposition in EC, while what is presupposed in both IC and OC is a (possible) conjunction.
Despite these differences, in both systems, the conditional is not truth functional, unlike the Stoic conditional.

Implications and Limits of Sequences

author: Alexandre Costa-Leite, Edelcio G. de Souza,
This paper analyzes the problem of implication and attempts to
characterize conditionals by a criterion of adequacy. A definition of implication
based on the notion of limit of an infinite sequence is proposed.