Dag Westerståhl

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A semantics may be compositional and yet partial, in the sense that not all well-formed expressions are assigned meanings by it. Examples come from both natural and formal languages. When can such a semantics be extended to a total one, preserving compositionality? This sort of extension problem was formulated in Hodges [9], and solved there in a particular(More)
The standard semantic definition of consequence with respect to a selected set X of symbols, in terms of truth preservation under replacement (Bolzano) or reinterpretation (Tarski) of symbols outside X, yields a function mapping X to a consequence relation ⇒X . We investigate a function going in the other direction, thus extracting the constants of a given(More)
A new formalism for predicate logic is introduced, with a non-standard method of binding variables, which allows a compositional formalization of certain anaphoric constructions, including ‘donkey sentences’ and crosssentential anaphora. A proof system in natural deduction format is provided, and the formalism is compared with other accounts of this type of(More)
Bolzano’s definition of consequence in effect associates with each set X of symbols (in a given interpreted language) a consequence relation ⇒X . We present this in a precise and abstract form, in particular studying minimal sets of symbols generating ⇒X . Then we present a method for going in the other direction: extracting from an arbitrary consequence(More)