Orvar Lorimer-Olsson: Power Lifting Logics – An Algebraic Approach to Semantic Set Lifting

It is hereby announced that Orvar Lorimer-Olsson will defend his Licentiate thesis in Logic on 27 November.

Title: Power Lifting Logics: An Algebraic Approach to Semantic Set Lifting

Principal Supervisor: Fredrik Engström
Opponent: Fan Yang, PhD, Assistant Professor
Examiner: Graham Leigh, Professor

Abstract

What properties of groups can be described from the properties of its individuals?  What is the meaning of a statement when considering a collection of possible interpretations? What happens to the structure of arguments if propositions can be both true and false simultaneously? 

All these questions are naturally treated formally by semantic set-lifting procedures. By lifting a semantic setup based on some set of semantic object to instead consider subsets, new semantics are formed with  increased expressibility and new logical properties. This Licentiate thesis investigates these type of semantic lifts and presents new constructions based on algebraic representations. By means of so called power  algebras, we present alternative variants to  the constructions called plurivalence  and team-semantic respectively. These new constructions are more independent of the  initial choices in semantic representation. In three articles these constructions are applied to describe and answer questions within three different directions in logic.