Dialogue semantics for logic are two-player logic games between a Proponent who puts forward a logical formula φ as valid or true and an Opponent who disputes this. An advantage of the dialogical approach is that it is a uniform framework from which different logics can be obtained through only small variations of the basic rules. We introduce the composition problem for dialogue games as the problem of resolving, for a set S of rules for dialogue games, whether the set (...) of S-dialogically valid formulas is closed under modus ponens. Solving the composition problem is fundamental for the dialogical approach to logic; despite its simplicity, it often requires an indirect solution with the help of significant logical machinery such as cut-elimination. Direct solutions to the composition problem can, however, sometimes be had. As an example, we give a set N of dialogue rules which is well-justified from the dialogical point of view, but whose set N of dialogically valid formulas is both non-trivial and non-standard. We prove that the composition problem for N can be solved directly, and introduce a tableaux system for N. (shrink)

Sentences about logic are often used to show that certain embedding expressions are hyperintensional. Yet it is not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. In this paper, I develop a formal system called hyperlogic that is designed to do just that. I provide a hyperintensional semantics for hyperlogic that doesn’t appeal to logically impossible worlds, as traditionally understood, but instead uses a shiftable parameter that determines the (...) interpretation of the logical connectives. I argue this semantics compares favorably to the more common impossible worlds semantics, which faces difficulties interpreting propositionally quantified logic talk. (shrink)

Humans communicate with different modalities. We offer an account of multi-modal meaning coordination, taking speech-gesture meaning coordination as a prototypical case. We argue that temporal synchrony (plus prosody) does not determine how to coordinate speech meaning and gesture meaning. Challenging cases are asynchrony and broadcasting cases, which are illustrated with empirical data. We propose that a process algebra account satisfies the desiderata. It models gesture and speech as independent but concurrent processes that can communicate flexibly with each other and exchange (...) the same information more than once. The account utilizes the ψ-calculus, allowing for agents, input-output-channels, concurrent processes, and data transport of typed λ-terms. A multi-modal meaning is produced integrating speech meaning and gesture meaning into one semantic package. Two cases of meaning coordination are handled in some detail: the asynchrony between gesture and speech, and the broadcasting of gesture meaning across several dialogue contributions. This account can be generalized to other cases of multi-modal meaning. (shrink)