Christian Straßer

A Deontic Logic Framework Allowing for Factual Detachment

Since our ethical and behavioral norms have a conditional form, it is of great importance that deontic logics give an account of deontic commitments such as ?A commits you to do/bring about B?. It is commonly agreed that monadic approaches are suboptimal for this task due to several shortcomings, for instance their falling short of giving a satisfactory account of ?Strengthening the Antecedent? or their difficulties in dealing with contrary-to-duty paradoxes. While dyadic logics are more promising in these respects, they have been criticized for not being able to model ?detachment?: A and the commitment under A to do B implies the actual obligation to do B. Lennart ?qvist asks in his seminal entry on deontic logic in the Handbook of Philosophical Logic: ?We seem to feel that detachment should be possible after all. But we cannot have things both ways, can we? This is the dilemma on commitment and detachment.? In this chapter I answer ?qvist?s question with ?Yes, we can?. I propose a general method to turn dyadic deontic logics in adaptive logics allowing for a defeasible factual detachment while paying special attention to specificity and contrary-to-duty cases. I show that a lot of controversy about detachment can be resolved by analysing different notions of unconditional obligations. The logical modeling of detachment is paradigmatically realized on basis of one of Lou Goble?s conflict tolerant CDPM logics.

An inconsistency-adaptive deontic logic for normative conflicts

We present the inconsistency-adaptive deontic logic DPr, a nonmonotonic logic for dealing with conflicts between normative statements. On the one hand, this logic does not lead to explosion in view of normative conflicts such as OA ∧ O ∼A, OA ∧ P ∼A or even OA ∧ ∼OA. On the other hand, DPr still verifies all intuitively reliable inferences valid in Standard Deontic Logic (SDL). DPr interprets a given premise set ‘as normally as possible’ with respect to SDL. Whereas some SDL-rules are verified unconditionally by DPr, others are verified conditionally. The latter are applicable unless they rely on formulas that turn out to behave inconsistently in view of the premises. This dynamic process is mirrored by the proof theory of DPr.

An adaptive logic framework for conditional obligations and deontic dilemmas

Lou Goble proposed powerful conditional deontic logics (CDPM) that are able to deal with deontic conflicts by means of restricting the inheritance principle. One of the central problems for dyadic deontic logics is to properly treat the restricted applicability of the principle “strengthening the antecedent”. In most cases it is desirable to derive from an obligation A under condition B, that A is also obliged under condition B and C. However, there are important counterexamples. Goble proposed a weakened rational monotonicity principle to tackle this problem. This solution is suboptimal as it is for some examples counter-intuitive or even leads to explosion. The paper identifies also other problems of Goble’s systems. For instance, to make optimal use of the restricted inheritance principle, in many cases the user has to manually add certain statements to the premises. An adaptive logic framework based on CDPM is proposed which is able to tackle these problems. It allows for certain rules to be applied as much as possible. In this way counter-intuitive consequences as well as explosion can be prohibited and no user interference is required. Furthermore, for non-conflicting premise sets the adaptive logics are equivalent to Goble’s dyadic version of standard deontic logic.

Abstract argumentation and explanation applied to scientific debates

Abstract argumentation has been shown to be a powerful tool within many fields such as artificial intelligence, logic and legal reasoning. In this paper we enhance Dung’s well-known abstract argumentation framework with explanatory capabilities. We show that an explanatory argumentation framework (EAF) obtained in this way is a useful tool for the modeling of scientific debates. On the one hand, EAFs allow for the representation of explanatory and justificatory arguments constituting rivaling scientific views. On the other hand, different procedures for selecting arguments, corresponding to different methodological and epistemic requirements of theory evaluation, can be formulated in view of our framework.

Sequent-based logical argumentation

We introduce a general approach for representing and reasoning with argumentation-based systems. In our framework arguments are represented by Gentzen-style sequents, attacks (conflicts) between arguments are represented by sequent elimination rules, and deductions are made according to Dung-style skeptical or credulous semantics. This framework accommodates different languages and logics in which arguments may be represented, allows for a flexible and simple way of expressing and identifying arguments, supports a variety of attack relations (including those that reflect relevance or quantitative considerations), and is faithful to standard methods of drawing conclusions by argumentation frameworks. Altogether, we show that argumentation theory may benefit from incorporating proof theoretical techniques and that different non-classical formalisms may be used for backing up intended argumentation semantics.

Towards the Proof-theoretic Unification of Dung’s Argumentation Framework

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’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.

Which style of reasoning to choose in the face of conflicting information

In the context of non-monotonic reasoning different kinds of consequence relations are defined for reasoning from (possibly) inconsistent information. Examples are consequence relations that are characterized in terms of maximal consistent subsets of the premise set. The strong consequences are those formulas that follow by Classical Logic from every maximal consistent subset. The weak consequences follow from some maximal consistent subset. The free consequences follow from the set of formulas that belong to every maximal consistent subset. In this paper the question is discussed which of these consequence relations should be applied in which reasoning context. First the concerns that are expressed in the literature with respect to the usefulness of the weak consequences are addressed. Then it is argued that making weak inferences is sensible for some application contexts, provided one has a (dynamic) proof theory for the corresponding consequence relation. Such a dynamic proof theory is what adaptive logics offer. Finally, all this is illustrated by means of a very simple adaptive logic reconstruction of the free, strong, and weak consequences.

An Adaptive Logic for Rational Closure

Lehmann and Magidor have proposed a powerful approach to model defeasible conditional knowledge: Rational Closure. Their account significantly strengthens previous proposals based on the so-called KLM-properties. In this chapter a dynamic proof theory for Rational Closure is presented.

Three formats of prioritized adaptive logics: a comparative study

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 ss 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.

Two Adaptive Logics of Norm-Propositions

We present two defeasible logics of norm-propositions (statements about norms) that (i) consistently allow for the possibility of normative gaps and normative conicts, and (ii) map each premise set to a suciently rich consequence set.