Arrows, Relevance, and Relations* - a podcast by MCMP Team

Michael Dunn (Bloomington) gives a talk at the MCMP Colloquium (25 June, 2013) titled "Arrows, Relevance, and Relations*". Abstract: The van Benthem-Venema "arrow logics" are abstractly well-motivated and have epistemic applications, e.g., to the logic of information flow and information update. I explore the relationships between the van Benthem-Venema semantics for arrow logics and the Routley-Meyer semantics for relevance logics, and show that there is a translation between the two. I will also briefly discuss the relationship to Barwise’s (1993) logic of "channels." I compare van Benthem’s version of the semantics for arrow logic aimed at relation algebras with my own generalization of the Routley-Meyer semantics aimed at the same target. I use my (1993, 2001) representation of relation algebras based on Routley-Meyer frames to give an equivalent representation of relation algebras based on frames for arrow logic. A philosophical interpretation is given to this representation as showing that each element of a relation algebra can be interpreted as a set of relations (not as a single relation –Lyndon showed this is impossible). This interpretation is thus a type level higher than the natural interpretation of an element as just a relation, and can be viewed in terms of interpreting each element as a relational database. The operations of a relation algebra can then be interpreted as operations combining relational databases.

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