## Compositionality in proof-theoretic semantics (2015)

(Heinrich Wansing, Ruhr Universität Bochum, DE)

In extensional many-valued logic, compositionality just means truth-functionality. The notion of truth is represented by a set of designated values, and semantical consequence (entailment) is defined as truth preservation from the premises of an inference to its conclusion. If falsity is understood as the absence of truth, the preservation of falsity is just the inverse of entailment viewed as truth preservation.

The distinction between designated values (representing truth) and anti-designated values (representing falsity), however, has given rise to additional conceptions of entailment such as quasi-entailment and plausibility-entailment, and preservation of falsity is no longer the inverse of the preservation of truth. The proof-theoretic counterpart of entailment is provability from a set of assumptions. In the talk I will argue that with truth and falsity as independent semantical categories, a compositional proof-theoretical account of the meaning of the logical operations requires a multiple-consequence setting, so that in addition to provability one has to employ a relation of dual provability or of disprovability. These considerations will be exemplified with an extended natural deduction framework.

Due to technical difficulties, the lecture had to be split into two parts and some minutes of the talk may be missing.

Below is a playlist:

The distinction between designated values (representing truth) and anti-designated values (representing falsity), however, has given rise to additional conceptions of entailment such as quasi-entailment and plausibility-entailment, and preservation of falsity is no longer the inverse of the preservation of truth. The proof-theoretic counterpart of entailment is provability from a set of assumptions. In the talk I will argue that with truth and falsity as independent semantical categories, a compositional proof-theoretical account of the meaning of the logical operations requires a multiple-consequence setting, so that in addition to provability one has to employ a relation of dual provability or of disprovability. These considerations will be exemplified with an extended natural deduction framework.

Due to technical difficulties, the lecture had to be split into two parts and some minutes of the talk may be missing.

Below is a playlist: