This contribution gives an outline of a game theoretic foundation of the logical structure inherent to the language of a science. Game theoretic approaches to a language were considered and developed by several authors. In this volume Saarinen examines the game theoretic semantics due to Hintikka and the dialog-game semantics due to Lorenzen. In the following I shall not re-examine the approaches by Hintikka and Lorenzen. However, some remarks about Lorenzen’s semantics are necessary since the game theoretic approach considered here (...) is essentially based on the idea of Lorenzen to use dialog-games for a foundation of logic.A systematic game theoretic presentation of the rules of a dialog game was given at first by Lorenz. Starting with certain structural rules which constitute the general scheme of a dialog, a further dialog rule is necessary in order to guarantee a finite game. (shrink)

The well-known proposal to consider the Lüders-von Neumann measurement as a non-classical extension of probability conditionalization is further developed. The major results include some new concepts like the different grades of compatibility, the objective conditional probabilities which are independent of the underlying state and stem from a certain purely algebraic relation between the events, and an axiomatic approach to quantum mechanics. The main axioms are certain postulates concerning the conditional probabilities and own intrinsic probabilistic interpretations from the very beginning. A (...) Jordan product is derived for the observables, and the consideration of composite systems leads to operator algebras on the Hilbert space over the complex numbers, which is the standard model of quantum mechanics. The paper gives an expository overview of the results presented in a series of recent papers by the author. For the first time, the complete approach is presented as a whole in a single paper. Moreover, since the mathematical proofs are already available in the original papers, the present paper can dispense with the mathematical details and maximum generality, thus addressing a wider audience of physicists, philosophers or quantum computer scientists. (shrink)