Transparency, transitivity or reflexivity
This thesis investigates logico-philosophical aspects of using either a non-transitive or a non-reflexive logic to obtain a logic of truth in which truth is transparent. It enquires into and rejects the claim that restricting transitivity of entailment to accommodate transparent truth suffices to make the connective tonk acceptable by arguing that tonk as defined in a cut-free sequent calculus requires in addition that the logic is non-reflexive to be uniquely defined, and develops a semantics for tonk based on models with two valuations which delivers a non-transitive and non-reflexive logic. It develops a cut-free sequent calculus and two kinds of semantics for a non-reflexive logic of truth in which truth is transparent, one based on trivalent models and one based on models with two valuations. It shows how to define a non-transitive, a paraconsistent and a paracomplete logic of truth on the models with two valuations and develops a cut-free sequent calculus that captures all four logics. It investigates to which extent the non-reflexive and the non-transitive logic of truth can express their own meta-inferences, and shows among other things how one can employ the paraconsistent and the paracomplete logic
Fjellstad, Andreas
Paradox ; Truth ; Entailment (Logic)
Transparency, transitivity or reflexivity. This thesis investigates logico-philosophical aspects of using either a non-transitive or a non-reflexive logic to obtain a logic of truth in which truth is transparent. It enquires into and rejects the claim that restricting transitivity of entailment to accommodate transparent truth suffices to make the connective tonk acceptable by arguing that tonk as defined in a cut-free sequent calculus requires in addition that the logic is non-reflexive to be uniquely defined, and develops a semantics for tonk based on models with two valuations which delivers a non-transitive and non-reflexive logic. It develops a cut-free sequent calculus and two kinds of semantics for a non-reflexive logic of truth in which truth is transparent, one based on trivalent models and one based on models with two valuations. It shows how to define a non-transitive, a paraconsistent and a paracomplete logic of truth on the models with two valuations and develops a cut-free sequent calculus that captures all four logics. It investigates to which extent the non-reflexive and the non-transitive logic of truth can express their own meta-inferences, and shows among other things how one can employ the paraconsistent and the paracomplete logic
transparency transitivity reflexivity investigates philosophical aspect use either non transitive non reflexive logic obtain logic truth truth transparent enquires reject claim restrict transitivity entailment accommodate transparent truth make connective acceptable argue define cut free calculus require addition logic non reflexive uniquely define develop semantics base model valuation delivers non transitive non reflexive logic develops cut free calculus two_kind semantics non reflexive logic truth truth transparent base model base model valuation show define non transitive logic truth model valuation develop cut free calculus capture logic investigates_extent non reflexive non transitive logic truth express meta inferences show among thing employ logic