Negation in the Logic of First Degree Entailment and Tonk

The dialogical framework is an approach to meaning that provides an alternative to both the model-theoretical and the proof-theoretical semantics. The dialogical approach to logic is not a logic but a semantic rule-based framework where different logics could be developed, combined or compared. But are there any constraints? Can we introduce rules ad libitum to define whatever logical constant? In the present paper I will explore the first conceptual moves towards the notion of Dialogical Harmony. Crucial for the dialogical approach are the following points 1. The distinction between local (rules for logical constants) and global meaning (included in the structural rules) 2. The player independence of local meaning 3. The distinction between the play level (local winning or winning of a play) and the strategic level (global winning; or existence of a winning strategy). 4. A notion of validity that amounts to winning strategy independently of any model instead of winning strategy for every model. 5. The notion of winning in a formal play instead of winning strategy in a model. In order to highlight these specific features of the dialogical approach to meaning I will discuss the dialogical analysis of tonk, some tonk-like operators and the negation of the logic of first-degree entailment . 1 [email protected].