University of Barcelona and Catholic University of Louvain.
Meaning postulates for substructural languages.
In this talk, I define meaning postulates (which build the constitution for a logic) for logical connectives in classical and substructural logics departing from the idea that logical connectives behave as punctuation marks of some logical consequence. I then show how logical connectives across and within different substructural logics coincide in their meaning postulates but diverge on the internalisation of both structural and meta-structural rules: structural rules distinguish connectives across logics while meta-structural rules distinguish connectives intra-logic. Finally, I discuss the consequences of the previous results on the meaning of logical connectives, refining the minimalist thesis that identifies the meaning of logical connectives with their introduction rules in a calculus.