@article {verdee2013degrees, title = {Degrees of inconsistency. Carefully combining classical and paraconsistent negation.}, year = {Submitted}, abstract = {

This paper is devoted to combining the negation of Classical Logic (CL) and the negation of Graham Priest{\textquoteright}s LP in a way that is faithful to central properties of the combined logics. We give a number of desiderata for a logic L which combines both negations. These desiderata include the following: (a) L should be truth functional, (b) L should be strictly non-explosive for the paraconsisent negation \~{} (i.e. if A and \~{}A both have a non-trivial set of consequences, then this should also be the case for the set containing both) and (c) L should be a conservative extension of CL and of LP. The desiderata are motivated by a particular property-theoretic perspective on paraconsistency. Next we devise the logic CLP. We present an axiomatization of this logic and three semantical characterizations (a non-deterministic semantics, an in nitely valued set-theoretic semantics and an in nitely valued semantics with integer numbers as values). We prove that CLP is the only logic satisfying all postulated desiderata. The in nitely valued semantics of CLP can be seen as giving rise to an interpretation in which inconsistencies and inconsistent properties come in degrees: not every sentence which involves inconsistencies is equally inconsistent.

}, author = {Verd{\'e}e, Peter} } @article {VanDePutte2012, title = {The Dynamics of Relevance: Adaptive Belief Revision}, journal = {Synthese}, volume = {187}, number = {1}, year = {2012}, month = {May}, pages = {1-42}, abstract = {

This paper presents eight (previously unpublished) adaptive logics for belief revision, each of which define a belief revision operation in the sense of the AGM framework. All these revision operations are shown to satisfy the six basic AGM postulates for belief revision, and Parikh’s axiom of Relevance. Using one of these logics as an example, we show how their proof theory gives a more dynamic flavor to belief revision than existing approaches. It is argued that this turns belief revision (that obeys Relevance) into a more natural undertaking, where analytic steps are performed only as soon as they turn out to be necessary in order to uphold certain beliefs.

}, doi = {10.1007/s11229-012-0116-9}, author = {Van De Putte, Frederik and Verd{\'e}e, Peter} }