DefLog: on the Logical Interpretation of Prima Facie Justified Assumptions

Abstract

Assumptions are often not considered to be definitely true, but only as prima facie justified. When an assumption is prima facie justified, there can for instance be a reason against it, by which the assumption is not actually justified. The assumption is then said to be defeated. This requires a revision of the standard conception of logical interpretation of sets of assumptions in terms of their models. Whereas in the models of a set of assumptions, all assumptions are taken to be true, an interpretation of prima facie justified assumptions must distinguish between the assumptions that are actually justified in the interpretation and those that are defeated.In the present paper, the logical interpretation of prima facie justified assumptions is investigated. The central notion is that of a dialectical interpretation of a set of assumptions. The basic idea is that a prima facie justified assumption is not actually justified, but defeated when its so-called dialectical negation is justified. The properties of dialectical interpretation are analyzed by considering partial dialectical interpretations, or stages, and by establishing the notion of dialectical justification. The latter leads to a characterization of the existence and multiplicity of the dialectical interpretations of a set of assumptions. Since dialectical interpretations are a variant of stable semantics, the results are relevant for existing work on nonmonotonic logic and defeasible reasoning, on which the present work builds.Instead of focusing on defeasible rules or arguments, the present approach is sentence-based. A particular innovation is the use of a conditional that is prima facie justified (just like other assumptions) instead of an inconclusive conditional.

Towards Formal Representation and Evaluation of Arguments

“…Formal aspects of argumentative structures are extensively investigated by those who deal with AI and defeasible reasoning, such as Pollock, who created OSCAR (1987), Vreeswijk (1997), and the creators of Deflog (Verheij 2003) and ASPIC? (Prakken 2010).…”

Proof with and without probabilities

“…The circumstances are also rebutting since the argument for the opposite conclusion ðevi; :innÞ is presumptively valid. Note that this example of rebutting defeat is defeat of a presumption (in the sense of Definition 2), hence can be regarded as a formalization of the idea of undermining defeat that is the basis of argumentation formalisms in which defeat is assumptionbased (Bondarenko et al 1997;Verheij 2003). See also the discussion of arguments with prima facie assumptions by Eemeren et al (2014).…”

Dialectical Argumentation with Argumentation Schemes: An Approach to Legal Logic

“…Recently I have developed a theory of dialectical argumentation and a corresponding logic of dialectical interpretation, called DEFLOG (Verheij 2003a). DEFLOG is sentence-based instead of rule-based, derivation-based or sequent-based, such as related formalisms (e.g., Reiter 1980;Pollock 1987Pollock , 1995Prakken and Sartor 1996).…”

“…Formally, DEFLOG'S dialectical interpretations of theories are a variant of Reiter's (1980) extensions of default theories, Gelfond and Lifschitz's (1988) stable models of logic programming, Dung's (1995) stable extensions of argumentation frameworks, and Bondarenko et al's (1997) stable extensions of assumption-based frameworks (see Verheij 2003a).…”

“…In terms of this notion an elegant criterion for the existence and multiplicity of dialectical interpretations can be given. The reader is referred to Verheij (2003a).…”