# Independence-Friendly Logic

The present work is a critical analysis of IF ("Independence-Friendly") logic, a logical system which was introduced by the Finnish philosopher Jaakko Hintikka towards the end of the '80s. It is a syntactical variant of Leon Henkin's logic of the branching quantifiers; Henkin's and Hintikka's logics are both characterized by the great freedom they allow in expressing functional dependences and independences among individual variables. Relationships of this kind were already implicit in classical logic; yet, by means of the classical first-order syntax only a small and rather arbitrary subset of all dependence and independence relationships can be expressed.

Hintikka claims that his logic plays a fundamental role in the foundations of mathematics; he even suggested that it may be the case that IF logic should replace first-order classical logic. The purpose of the present work is a formal clarification of the definition and peculiarities of Independence-Friendly logic, aimed at a full understanding of Hintikka's assertions. This seems to be a necessary step towards the confirmation or refutation of Hintikka's claims.

Chapter One introduces Hintikka's syntax, and the most traditional semantics for IF logic; then comes an overview of the main syntactical variants which occur in literature. Following Hintikka, we describe another semantics, which is based on Game Theory; we prove its equivalence with the previous semantics. We prove that IF logic is also equivalent with a significant fragment of second-order logic. Then, we present a generalized IF logic, and its semantics as formalized by W.Hodges; we explain the relationship which bounds together IF and generalized IF logic; through Hodges' semantics we obtain an answer to the problem of "compositionality" of IF logic.

Chapter Two is devoted to an analysis of the differences between IF and first-order classical logic. The focus is mainly on the difficulties which arise in the treatment of concepts such as negation, equivalence and implication. Towards the end of the chapter, we shift our attention to some relevant remarks of Theo Janssen.

A few of his remarks reveal bizarre features of IF logic, and cast doubts on its meanings. Others seem to be simply wrong; yet, a careful examination of these argumentations shows that IF logic is extremely sensitive to slight changes in syntax.

In Chapter Three we make use of the formalization which was developed so far in order to re-examine some of the main claims of Hintikka's "The Principles of Mathematics Revisited".

Laurea liv.II (specialistica)

Facoltà: Scienze Matematiche, Fisiche e Naturali

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Autore:
Fausto Barbero
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Composta da 70 pagine.

Questa tesi ha raggiunto 261 click dal 27/02/2009.

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