A Logic for prioritized normative reasoning

In this article we present the logic MP⊏ that explicates reasoning on the basis of prioritized obligations. Although formal criteria to handle prioritized obligations have been formulated in the literature, little attention has been paid to the actual (non-monotonic) reasoning that makes use of these criteria. The dynamic proof theory of MP⊏ fills this lacuna. This article focuses on premise sets consisting of possibly conflicting prima facie obligations that have a modular order. MP⊏ allows to derive—inter alia—the actual, all-things-considered obligations from such premise sets. It is defined in the format of lexicographic adaptive logics from [34], whence a rich meta-theory is immediately available (e.g. soundness and completeness, idempotence, reflexivity, etc.). In addition, we establish some meta-theoretic results that are specific to the context of prioritized obligations. With the aid of concrete examples, we illustrate properties of MP⊏ which improve on other existing criteria for prioritized obligations.

[1]  Daniel Lehmann,et al.  Another perspective on default reasoning , 1995, Annals of Mathematics and Artificial Intelligence.

[2]  David Makinson.  Propositional relevance through letter-sharing , 2009, J. Appl. Log..

[3]  Diderik Batens,et al.  A Universal Logic Approach to Adaptive Logics , 2007, Logica Universalis.

[4]  Christian Straßer.  An adaptive logic framework for conditional obligations and deontic dilemmas , 2010 .

[5]  G. Priest.  In Contradiction: A Study of the Transconsistent , 1987 .

[6]  Christian Straßer,et al.  Non-Adjunctive Deontic Logics That Validate Aggregation as Much as Possible∗ , 2010 .

[7]  R Fox,et al.  Moral dilemmas. , 1998, Journal of the Royal Society of Medicine.

[8]  Lou Goble,et al.  A logic for deontic dilemmas , 2005, J. Appl. Log..

[9]  Liza Verhoeven.  Proof Theories for Some Prioritized Consequence Relations , 2003 .

[10]  Alexa Zellentin,et al.  3 The right and the good , 2012 .

[11]  Gabriella Pigozzi,et al.  Ten Philosophical Problems in Deontic Logic , 2007, Normative Multi-agent Systems.

[12]  Carlos E. Alchourrón,et al.  Hierarchies of Regulations and their Logic , 1981 .

[13]  Leon van der Torre,et al.  Constraints for Input/Output Logics , 2001, J. Philos. Log..

[14]  Frederik Van De Putte,et al.  The dynamics of relevance: adaptive belief revision , 2012, Synthese.

[15]  Lou Goble,et al.  Preference semantics for deontic logic part I — Simple models , 2003 .

[16]  Peter K. Schotch,et al.  Non - Kripkean Deontic Logic , 1981 .

[17]  Christian Straßer,et al.  A deontic logic framework allowing for factual detachment , 2011, J. Appl. Log..

[18]  Daniel Lehmann,et al.  What does a Conditional Knowledge Base Entail? , 1989, Artif. Intell..

[19]  John F. Horty,et al.  Reasoning with Moral Conflicts , 2003 .

[20]  Christian Straßer,et al.  An Inconsistency-Adaptive Deontic Logic for Normative Conflicts , 2012, Journal of Philosophical Logic.

[21]  Frederik Van De Putte,et al.  Avoiding Deontic Explosion by Contextually Restricting Aggregation , 2010, DEON.

[22]  Guido Boella,et al.  Institutions with a hierarchy of authorities in distributed dynamic environments , 2008, Artificial Intelligence and Law.

[23]  Lou Goble,et al.  Multiplex semantics for deontic logic , 2000 .

[24]  Newton C. A. da Costa,et al.  On paraconsistent deontic logic , 1986 .

[25]  Bernhard Nebel,et al.  Belief Revision: Syntax based approaches to belief revision , 1992 .

[26]  Lou Goble,et al.  Preference semantics for deontic logic part II – Multiplex models , 2004 .

[27]  John F. Horty,et al.  Moral dilemmas and nonmonotonic logic , 1994, J. Philos. Log..

[28]  Christian Straßer,et al.  Extending the standard format of adaptive logics to the prioritized case , 2012 .

[29]  Lou Goble.  A Proposal for Dealing with Deontic Dilemmas , 2004, DEON.

[30]  R. Parikh.  Beliefs, belief revision, and splitting languages , 1999 .

[31]  Edwin D. Mares.  Andersonian deontic logic , 2008 .

[32]  Jörg Hansen.  Prioritized conditional imperatives: problems and a new proposal , 2007, Autonomous Agents and Multi-Agent Systems.

[33]  B. V. Fraassen.  Values and the Heart's Command , 1973 .

[34]  David Makinson,et al.  Parallel interpolation, splitting, and relevance in belief change , 2007, Journal of Symbolic Logic.

[35]  Jörg Hansen,et al.  Deontic logics for prioritized imperatives , 2006, Artificial Intelligence and Law.