Reinhard Muskens: Calculi for Logics of Thinking Computers and Computer Networks

Lecture by Reinhard Muskens (Tilburg), organized by Grolog

In a now famous paper published in 1976, Nuel Belnap argues that computer reasoning should be modeled on the basis of a four-valued logic in which each value is a combination of the two classical values. Belnap also considers two lattices on these four values, one corresponding to increase in truth and non-falsity, the other to increase of information. Together these two lattices form what is now called a /bilattice/.

More recently Yaroslav Shramko and Heinrich Wansing (2005) have in a sense repeated Belnap's move, arguing that the logic of the reasoning of computer /networks/ should be 16-valued, with each value corresponding to a set of Belnap's values. They consider what is called a /trilattice/ on these 16 values and distinguish between an entailment relation based on the notion of truth and one based on falsity. These two relations are not equal or each other's inverses.

In this talk, which reports on joint work with Stefan Wintein, I will look at syntactic characterisations for these logics, with particular reference to...(continue reading)...