Valuations (bi, tri, and tetra)

David Ripley (University of Connecticut)

Dave Ripley (UConn) will present "Valuations (bi, tri, and tetra)" at 11 in Old Quad G14.

Abstract: This paper draws together and systematizes a number of results about valuations and the kinds of consequence relations that they can present. A number of results that are more or less widely-known for two-valued valuations and RMT logics (logics that are Reflexive, Monotonic, and Transitive, in appropriate senses) are special cases of more general facts. Where this has been noticed in the literature, it is typically taken up piecemeal if at all. This paper attempts a more systematic overview, and includes some (although not terribly many) new results needed to fill in a broad picture. We work with both Set-Set and Set-Fmla arguments, and four different kinds of valuation (two-valued, two kinds of three-valued, and four-valued). This results in eight lattices of "consequence relations". We close by considering adding connectives to the language to witness the bilattice structure of valuations. This is joint work with Rohan French  (but the presentation is very much not Rohan-approved (which is certainly not to say that it's Rohan-disapproved (yet?)))