Speaker
Christian Wurm
Heinrich Heine Universität Düsseldirf
Talks at this conference:
Tuesday, 18:10, J330 
Finite Models for NonCommutative Ambiguity Logics 
We speak of ambiguity (in the linguistic sense) if one sign (word, phrase, sentence) has two or more clearly distinct meanings. Recent work on logics with an explicit representation of ambiguity (see [2,3]) has shown that there are two kinds of logics: those who are closed under transitive inference or more generally under the rule (cut), and those which are closed under uniform substitution of atoms. Having both properties (which are both basic requirements of abstract logics in the sense of Tarski) – together with the most basic properties of ambiguity – leads to triviality of the logic. Moreover, every ambiguity logic comes in two versions: a) with commutative ambiguity (basically, readings can be conceived of as sets), and b) with noncommutative ambiguity (readings can be conceived of as an ordered list). Two ambiguity logics have received a particular interest (in both variants): DAL (introduced in [1], closed under (cut)) and and TAL (see [2], closed under uniform substitution), with their commutative variants cDAL and cTAL. From a semantic point of view, cDAL and cTAL are considerably simpler: there is a straightforward semantics for both based on finite classical models, which allows to prove two key results (for proofs see [1,3]):
In this talk, we pesent a sound and complete semantics with finite models for noncommutative DAL and TAL, which allows to transfer the two results to this case. The models are sets of strings with certain languagetheoretic closure properties. Bibliography
