Compositionality in Context
Alexandru Baltag, Johan van Benthem, Dag Westerstähl

Abstract:
Compositionality is a principle used in logic, philosophy, mathematics, linguistics, and computer science for assigning meanings to language ex- pressions in a systematic manner following syntactic construction, thereby allowing for a perspicuous algebraic view of the syntax-semantics inter- face. Yet the status of the principle remains under debate, with positions ranging from compositionality always being achievable to its having gen- uine empirical content. This paper attempts to sort out some major issues in all this from a logical perspective. First, we stress the fundamental har- mony between Compositionality and its apparent antipode of Contextu- ality that locates meaning in interaction with other linguistic expressions and in other settings than the actual one. Next, we discuss basic fur- ther desiderata in designing and adjudicating a compositional semantics for a given language in harmony with relevant contextual syntactic and semantic cues. In particular, in a series of concrete examples in the realm of logic, we point out the dangers of over-interpreting compositional solu- tions, the ubiquitous entanglement of assigning meanings and the key task of explaining given target inferences, and the dynamics of new language design, illustrating how even established compositional semantics can be rethought in a fruitful manner. Finally, we discuss some fresh perspec- tives from the realm of game semantics for natural and formal languages, the general setting for Samson Abramsky’s influential work on program- ming languages and process logics. We highlight outside-in coalgebraic perspectives on meanings as finite or infinitely unfolding behavior that might challenge and enrich current discussions of compositionality.