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On the transparency of defeasible logics: Equivalent premise sets, equivalence of their extensions, and maximality of the lower limit
"... 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 ..."
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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. 1 Formats for Logics for Plausible Reasoning This paper has a specific and a more general aim. The specific aim is related to determining whether two premise sets are equivalent with respect to logics that explicate defeasible reasoning forms—henceforth DRF. We shall show that adaptive logics are superior to other formats in this respect. The more general aim is to highlight the advantages of the adaptive logic program with respect to other approaches to DRF. Let us compare the situation with Tarski logics, logics the consequence relation of which is Reflexive, Transitive and Monotonic. A variety of formulations has been developed: axiomatic, Fitchstyle, Gentzenstyle, etc. Each of these have their stronger points. The variety, however, is only apparent. First, there are relatively standard procedures that, for most logics, enable one to turn one formulation into another. Next, the different formulations are at best different ∗ Peter Verdée is a postdoctoral fellow of the Fund for Scientific Research – Flanders.
On the Transparency of Defeasible Logics: Equivalent Premise Sets, Equivalence of Their Extensions, and Maximality of the
, 2009
"... 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 ..."
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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. 1 Formats for Logics for Plausible Reasoning This paper has a specific and a more general aim. The specific aim is related to determining whether two premise sets are equivalent with respect to logics that explicate defeasible reasoning forms—henceforth DRF. We shall show that adaptive logics are superior to other formats in this respect. The more general aim is to highlight the advantages of the adaptive logic program with respect to other approaches to DRF. Let us compare the situation with Tarski logics, logics the consequence relation of which is Reflexive, Transitive and Monotonic. A variety of formulations has been developed: axiomatic, Fitchstyle, Gentzenstyle, etc. Each of these have their stronger points. The variety, however, is only apparent. First, there ∗Research for this paper was supported by subventions from Ghent University and from the Fund for Scientific Research – Flanders. †Peter Verdée is a postdoctoral fellow of the Fund for Scientific Research – Flanders.
A Proof Procedure for Adaptive Logics
"... In this paper I present a procedure that generates adaptive proofs for finally derivable adaptive logic consequences. The proof procedure for the inconsistency adaptive logic CLuNr is already presented in [10]. In this paper the procedure for CLuNm is presented and the results for both logics are ge ..."
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In this paper I present a procedure that generates adaptive proofs for finally derivable adaptive logic consequences. The proof procedure for the inconsistency adaptive logic CLuNr is already presented in [10]. In this paper the procedure for CLuNm is presented and the results for both logics are generalized to all adaptive logics, on the presupposition that there exists a total proof procedure for lower limit logic derivability of the adaptive logic and a finite set of problem relevant abnormalities.