@article {3152459, title = {Three formats of prioritized adaptive logics: a comparative study}, journal = {Logic journal of the IGPL}, volume = {21}, year = {2013}, pages = {127{\textendash}159}, abstract = {

A broad range of defeasible reasoning forms has been explicated by prioritized adaptive logics. However, the relative lack in meta-theory of many of these logics stands in sharp contrast to the frequency of their application. This article presents the first comparative study of a large group of prioritized adaptive logics. Three formats of such logics are discussed: superpositions of adaptive logics, hierarchic adaptive logics from F. Van De Putte (2011, Log. J. IGPL, doi:10.1093/jigpal/jzr025) and lexicographic adaptive logics from F. Van De Putte and C. Stra\&\#223;er (2012, Log. Anal., forthcoming). We restrict the scope to logics that use the strategy Minimal Abnormality. It is shown that the semantic characterizations of these systems are equivalent and that they are all sound with respect to either of these characterizations. Furthermore, sufficient conditions for the completeness and equivalence of the consequence relations of the three formats are established. Some attractive properties, including Fixed Point and the Deduction Theorem, are shown to hold whenever these conditions are obeyed.

}, issn = {1367-0751}, doi = {http://dx.doi.org/10.1093/jigpal/jzs004}, author = {Van De Putte, Frederik and Stra{\ss}er, Christian} } @article {3152453, title = {Two adaptive logics of norm-propositions}, journal = {JOURNAL OF APPLIED LOGIC}, volume = {11}, number = {2}, year = {2013}, pages = {147{\textendash}168}, abstract = {

We present two defeasible logics of norm-propositions (statements about norms) that (i) consistently allow for the possibility of normative gaps and normative conflicts, and (ii) map each premise set to a sufficiently rich consequence set. In order to meet (i), we define the logic LNP, a conflict- and gap-tolerant logic of norm-propositions capable of formalizing both normative conflicts and normative gaps within the object language. Next, we strengthen LNP within the adaptive logic framework for non-monotonic reasoning in order to meet (ii). This results in the adaptive logics LNPrLNPr and LNPmLNPm, which interpret a given set of premises in such a way that normative conflicts and normative gaps are avoided ‘whenever possible’. LNPrLNPr and LNPmLNPm are equipped with a preferential semantics and a dynamic proof theory.

}, issn = {1570-8683}, doi = {http://dx.doi.org/10.1016/j.jal.2013.02.001}, author = {Beirlaen, Mathieu and Stra{\ss}er, Christian} } @article {CJM:demi, title = {Tolerating Deontic Conflicts by Adaptively Restricting Inheritance}, journal = {Logique et Analyse}, volume = {219}, year = {2012}, pages = {477-506}, abstract = {

In order to deal with the possibility of deontic conflicts Lou Goble developed a group of logics DPM that are characterized by a restriction of the inheritance principle. While they approximate the deductive power of standard deontic logic, they do so only if the user adds certain statements to the premises. By adaptively strengthening the DPM logics, this paper presents logics that overcome this shortcoming. Furthermore, they are capable of modeling the dynamic and defeasible aspect of our normative reasoning by their dynamic proof theory. This way they enable us to have a better insight in the relations between obligations and thus to localize deontic conflicts.

}, author = {Stra{\ss}er, Christian and Meheus, Joke and Beirlaen, Mathieu} } @article {1101225, title = {Towards the proof-theoretic unification of {D}ung{\textquoteright}s argumentation framework: an adaptive logic approach}, journal = {Journal of logic and computation}, volume = {21}, number = {2}, year = {2011}, pages = {133{\textendash}156}, abstract = {

The article presents a unifying adaptive logic framework for abstract argumentation. It consists of a core system for abstract argumentation and various adaptive logics based on it. These logics represent in an accurate sense all standard extensions defined within Dung{\textquoteright}s abstract argumentation system with respect to sceptical and credulous acceptance. The models of our logics correspond exactly to specific extensions of given argument systems. Additionally, the dynamics of adaptive proofs mirror the argumentative reasoning of a rational agent. In particular, the presented logics allow for external dynamics, i.e. they are able to deal with the arrival of new arguments and are therefore apt to model open-ended argumentations by providing provisional conclusions.

}, issn = {0955-792X}, url = {http://dx.doi.org/10.1093/logcom/exq015}, author = {Stra{\ss}er, Christian and {\v S}e{\v s}elja, Dunja} } @article {strasser2010towards, title = {Towards more conflict-tolerant deontic logics by relaxing the interdefinability between obligations and permissions}, year = {2010}, abstract = {

While conflict-tolerant logics (CTDLs) usually allow for obligation- obligation conflicts, they fall short of tolerating obligation-permission con- flicts (OP-conflicts) of the type OA \&\#8743; P\&\#172; A. Moreover, for the sake of conflict-tolerance these logics usually do not validate the very intuitive principle (D), OA \&\#8835; PA. We demonstrate in this paper that by relaxing the interdefinability between obligations and permission PA =df \&\#172;O\&\#172;A that is characteristic for most deontic logics, the logics get more conflict-tolerant since they allow for OP-conflicts. Moreover, this way they can be equipped with (D) without the need to sacrifice conflict-tolerance. In this paper we offer a generic procedure that transforms a given CTDL into a logic that tolerates OP-conflicts and validates (D).

}, author = {Stra{\ss}er, Christian and Beirlaen, Mathieu} } @article {DC\&P:tdl, title = {On the Transparency of Defeasible Logics: Equivalent Premise Sets, Equivalence of Their Extensions, and Maximality of the Lower Limit}, journal = {Logique et Analyse}, volume = {207}, year = {2009}, pages = {281{\textendash}304}, abstract = {

For Tarski logics, there are simple criteria that enable one to conclude that two premise sets are equivalent. We shall show that the very same criteria hold for adaptive logics, which is a major advantage in comparison to other approaches to defeasible reasoning forms.
A related property of Tarski logics is that the extensions of equivalent premise sets with the same set of formulas are equivalent premise sets. This does not hold for adaptive logics. However a very similar criterion does.
We also shall show that every monotonic logic weaker than an adaptive logic is weaker than the lower limit logic of the adaptive logic or identical to it. This highlights the role of the lower limit for settling the adaptive equivalence of extensions of equivalent premise sets.

}, author = {Batens, Diderik and Stra{\ss}er, Christian and Verd{\'e}e, Peter} }