Tero Tulenheimo

From Games to Dialogues and Back

In this article two game-theoretically flavored approaches to logic are systematically compared: dialogical logic founded by Paul Lorenzen and Kuno Lorenz, and the game-theoretical semantics of Jaakko Hintikka. For classical proposi-tional logic and for classical first-order logic, an exact connection between ‘in-tuitionistic dialogues with hypotheses’ and semantic games is established. Various questions of a philosophical nature are also shown to arise as a result of the comparison, among them the relation between the model-theoretic and proof-theoretic approaches to the philosophy of logic and mathematics.

Games: Unifying Logic, Language, and Philosophy

Give us 5 minutes and we will show you the best book to read today. This is it, the games unifying logic language and philosophy that will be your best choice for better reading book. Your five times will not spend wasted by reading this website. You can take the book as a source to make better concept. Referring the books that can be situated with your needs is sometime difficult. But here, this is so easy. You can find the best thing of book that you can read.This volume presents mathematical game theory as an interface between logic and philosophy. It provides a discussion of various aspects of this interaction, covering new technical results and examining the philosophical insights that these have yielded. Organized in four sections it offers a balanced mix of papers dedicated to the major trends in the field: the dialogical approach to logic, Hintikka-style game-theoretic semantics, game-theoretic models of various domains (including computation and natural language) and logical analyses of game-theoretic situations. This volume will be of interest to any philosopher concerned with logic and language. It is also relevant to the work of argumentation theorists, linguists, economists, computer scientists and all those concerned with the foundational aspects of these disciplines.

Partially ordered connectives and ∑ 1 1 on finite models

In this paper we take up the study of Henkin quantifiers with boolean variables [4], also known as partially ordered connectives [19]. We consider first-order formulae prefixed by partially ordered connectives, denoted D, on finite structures. D is characterized as a fragment of second-order existential logic

Unity, Truth and the Liar

{\sum^1_1\heartsuit}

Hybrid Logic Meets IF Modal Logic

, whose formulae do not allow existential variables as arguments of predicate variables. By means of a game theoretic argument, it is shown that

Partially Ordered Connectives and Monadic Monotone Strict NP

{\sum^1_1\heartsuit}

Cross-World Identity, Temporal Quantifiers and the Question of Tensed Contents

harbors a strict hierarchy induced by the arity of predicate variables, and that it is not closed under complementation. It is further shown that allowing at most one existential variable to appear as an argument of a predicate variable, already yields a logic coinciding with full ∑

On the existence of a modal-logical basis for monadic second-order logic

^{\rm 1}_{\rm 1}

Negation and Temporal Ontology

.

The two faces of compatibility with justified beliefs

The Liar Paradox challenges logicians’ and semanticists’ theories of truth and meaning. Modern accounts of paradoxes in formal semantics offer solutions through the hierarchy of object language and metalanguage. Yet this solution to the Liar presupposes that sentences have unique meaning. This assumption is non-controversial in formal languages, but an account of how “hidden meaning” is made explicit is necessary to any complete analysis of natural language. Since the Liar Paradox presents itself as a sentence uniting contradictory meanings, appreciating how they can be united in a single sentence may provide new insights into this and other paradoxes. This volume includes a target paper, taking up the challenge to revive, within a modern (formal) framework, a medieval solution to the Liar Paradox which did not assume Uniqueness of Meaning. Stephen Read, author of the target paper, attempts to formally state a theory of truth that dates back to the 14th century logician Thomas Bradwardine; the theory offers a solution to the Liar Paradox in which the Liar sentence turns out to be false. The rest of the volume consists of papers discussing and/or challenging Read’s – and Bradwardine’s -- views one the one hand, and papers addressing the doctrinal and historical background of medieval theories of truth on the other hand. It also includes a critical edition of Heytesbury’s treatise on insolubles, closely related to Bradwardine’s view. Including formal, philosophical and historical discussions, this volume intends to renew the debate about paradoxes and theory of truth, and to show that the interest of earlier medieval work is not merely historical but, on the contrary, still relevant for modern, formal semantic theory. It is of interest for both professional philosophers and advanced students of philosophy.