LUW May 11: On Nonmonotonic Consequence Relations by Alexei Muravitsky

jean-yves beziau beziau100 at
Mon May 9 18:04:14 EDT 2022

This coming Wednesday, May 11 at 4pm CET,
we will have the next session of the Logica Universalis with a talk by
Alexei Muravitsky
Louisiana Scholars’ College, Northwestern State University, USA
Title: "On Nonmonotonic Consequence Relations"
Abstract: We discuss nonmonotonic reasoning in terms of consequence
relations and corresponding operators. Based on the matrix consequence that
gives the monotonic case, we define a restricted matrix consequence that
illustrates the nonmonotonic case. The latter is a generalization of the
relation of logical friendliness introduced by D. Makinson. We prove that
any restricted single matrix consequence, although it may be nonmonotonic,
is always weakly monotonic and, in the case of a finite matrix, the
restricted matrix consequence is very strongly finitary. Further, by
modifying the definition of logical friendliness relation formulated
specifically in a proof-theoretic manner, we show a possibility of
obtaining other reflexive nonmonotonic consequence relations, for which a
limited result towards finitariness is proved. This leads to numerous
questions about nonmonotonic consequence relations in the segment between
the monotonic consequence relation based on intuitionistic propositional
logic and logical friendliness.

Everybody is welcome to join:

Jean-Yves Beziau
Organizer of LUW and President of LUA
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