Logical Consequence Explicated in Terms of Cognitive Attitudes - a podcast by MCMP Team

Joao Marcos (UFRN) gives a talk at the MCMP Colloquium (5 June, 2014) titled "Logical consequence explicated in terms of cognitive attitudes". Abstract: The received notions of logical consequence, either introduced by semantical means or by way of some convenient proof formalism, or even studied in their own right as abstract relations/operations between sentences or collections of sentences, are often explicated in terms of standard judgments such as assertion and refutation/denial. As a matter of fact, from the semantical viewpoint such judgments are often confused with truth-values. For a fresh view on the matter, we propose substituting judgments by a richer collection of primitive cognitive attitudes concerning acceptance or rejection, by an agent, of a given piece of information, and organize such attitudes into an opposition structure from which we show how to extract a generous bidimensional notion of entailment, henceforth called B-entailment, that generalizes the well-known approaches by Tarski, by Scott, and by
Shoesmith&Smiley ([7]). We study and prove a general characterization result about the underlying abstract consequence relations in terms of a bilattice-based structure of truth-values, show that it extends earlier results by G. Malinowski and S. Frankowski ([6,4]), and show how this connects to older and newer research on the structure of truth-values or of the space of valuations ([2,8,5]). Finally, we also prove a normal form result that shows how the B-entailment formalism is expressive enough so as to define any 4-valued (partial) nondeterministic matrix ([1,3]). This reports on joint work with Carolina Blasio and Carlos Caleiro.

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