@article {DT:ddp, title = {Direct Dynamic Proofs For the {R}escher{\textendash}{M}anor Consequence Relations: The Flat Case}, journal = {Journal of Applied Non-Classical Logics}, volume = {12}, year = {2002}, pages = {63{\textendash}84}, abstract = {

It was shown in \cite{D:unific} that the flat Rescher{\textendash}Manor consequence relations{\textendash}-the Free, Strong, Argued, C-Based, and Weak consequence relation{\textendash}-are all characterized by special applications of inconsistency-adaptive logics defined from the paraconsistent logic CLuN. As as result, these consequence relations are provided with a dynamic proof theory. In the present paper we show that the detour via an inconsistency-adaptive logic is not necessary. We present a direct dynamic proof theory, formulated in the language of Classical Logic, and prove its adequacy.

}, author = {Batens, Diderik and Vermeir, Timothy} } @article {Vermeir_fromwffs, title = {From Wffs to Clauses: Transforming Wffs in Clauses Without Loss of Meaning}, year = {2002}, abstract = {

This paper is the rst step into the research of inconsistency-adaptive logic programming. It will be shown here that a mapping can be dened for well formed formulas to logic programming clauses in a paraconsistent environment, and without loss of information. Furthermore, this mapping is a purely mechanical procedure that can be implemented with ease on a computer.

}, author = {Vermeir, Timothy} } @incollection {vermeir2002inconsistency, title = {An Inconsistency-Adaptive Proof Procedure for Logic Programming}, booktitle = {Paraconsistency. The Logical Way to the Inconsistent}, year = {2002}, pages = {323-340}, publisher = {Marcel Dekker}, address = {New York}, abstract = {

It is the goal of this paper to de ne a paraconsistent proof procedure that has the best of two mechanisms, in casu logic programming and inconsistency-adaptive logics. From logic programming we will maintain the ease of computing, and from adaptive logics their paraconsistency, dynamics and non-monotonicity. This will be done by combining the notion of competitor from logic programming together with the conditionallity that is common in all adaptive proofs.

}, author = {Vermeir, Timothy}, editor = {Carnielli, Walter A. and Coniglio, Marcelo E. and Loffredo D{\textquoteright}Ottaviano, Itala M.} } @article {Vermeir_inconsistency-adaptivearithmetic, title = {Inconsistency-adaptive Arithmetic}, journal = {Logique et Analyse}, volume = {42}, number = {167-168}, year = {2000}, pages = {221-241}, abstract = {

In this article, it is shown that inconsistent arithmetic, as proposed by Jean Paul Van Bendegem and Graham Priest, does not have all the properties they claim the system has. The search for a system of inconsistent arithmetic that does have the intended properties, will lead us through different axiomatizations and different logics, the final result being inconsistency-adaptive arithmetic.

}, author = {Vermeir, Timothy} }