Frederik Van De Putte

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.

The dynamics of relevance: adaptive belief revision

This paper presents eight (previously unpublished) adaptive logics for belief revision, each of which define a belief revision operation in the sense of the AGM framework. All these revision operations are shown to satisfy the six basic AGM postulates for belief revision, and Parikh’s axiom of Relevance. Using one of these logics as an example, we show how their proof theory gives a more dynamic flavor to belief revision than existing approaches. It is argued that this turns belief revision (that obeys Relevance) into a more natural undertaking, where analytic steps are performed only as soon as they turn out to be necessary in order to uphold certain beliefs.

Coarse deontic logic

Cariani [7] has proposed a semantics for ought that combines two features: (i) it invalidates Inheritance in a principled manner; (ii) it allows for coarseness, which means that ought(φ) can be true even if there are specific ways of making φ true that are (intuitively speaking) impermissible. We present a family of multi-modal logics based on Cariani’s proposal and a more recent critique by Bronfmann&Dowell [4]. We study their formal properties in detail and show how they can be translated into normal multi-modal logics. Using well-known techniques, we establish a sound and (strongly) complete axiomatization for each of these and show them to satisfy the finite model property. In addition, we compare them to existing approaches in the deontic logic literature — most notably Anglberger et al.’s logic of obligation as weakest permission and Horty’s deontic stit logic.

Adaptive Logic Characterizations of Input/Output Logic

We translate unconstrained and constrained input/output logics as introduced by Makinson and van der Torre to modal logics, using adaptive logics for the constrained case. The resulting reformulation has some additional benefits. First, we obtain a proof-theoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our framework naturally gives rise to useful variants and allows to express important notions that go beyond the expressive means of input/output logics, such as violations and sanctions.

Adaptive strategies and finite-conditional premise sets

The standard format of adaptive logics makes use of two so-called strategies: reliability and minimal abnormality. While these are fairly well-known and frequently applied, the question of whether and when the two strategies are equi-epressive has so far remained unaddressed. In this paper, we show that for a specific, yet significant class of premise sets, the consequence set of an adaptive logic that uses the minimal abnormality strategy can be expressed by another adaptive logic that uses the reliability strategy. The basic idea is that we close the set of abnormalities under conjunction. We show that the consequence sets obtained by both logics from a premise set Γ is identical if and only if Γ is finite-conditional. The latter property is specified in terms of a well-known characterization of minimal abnormality. In addition, we discuss other (stronger) properties of premise sets that have been considered in the literature, showing each of them to imply finite-conditionality.

Default Assumptions and Selection Functions: A Generic Framework for Non-monotonic Logics

We investigate a generalization of so-called default-assumption consequence relations, obtained by replacing the consequence relation of classical logic with an arbitrary supraclassical, compact Tarski-logic, and using arbitrary selection functions on sets of sets of defaults. Both generalizations are inspired by various approaches in non-monotonic logic and belief revision. We establish some meta-theoretic properties of the resulting systems. In addition, we compare them with two other frameworks from the literature on non-monotonic logic, viz. adaptive logics and selection semantics.

A logic for the discovery of deterministic causal regularities

We present a logic,

OBLIGATION AS WEAKEST PERMISSION: A STRONGLY COMPLETE AXIOMATIZATION

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