Non-monotonic reasoning with normative conflicts in multi-agent deontic logic

We present two multi-agent deontic logics that consistently accommodate various types of normative conflicts. Its language features modal operators for obligation and permission, and for the realization of individual and collective actions. The logic is non-classical since it makes use of a paraconsistent and paracomplete negation connective. Moreover, it is non-monotonic due to its definition within the adaptive logics framework for defeasible reasoning. The logic is equipped with a defeasible proof theory and semantics.

[1]  Krister Segerberg,et al.  Getting started: Beginnings in the logic of action , 1992, Stud Logica.

[2]  John-Jules Ch. Meyer,et al.  A different approach to deontic logic: deontic logic viewed as a variant of dynamic logic , 1987, Notre Dame J. Formal Log..

[3]  Sven Ove Hansson,et al.  The Structure of Values and Norms , 2007, Cambridge Studies in Probability, Induction and Decision Theory.

[4]  Mathieu Beirlaen,et al.  Tolerating deontic conflicts by adaptively restricting inheritance , 2012 .

[5]  Matthew L. Ginsberg,et al.  Readings in Nonmonotonic Reasoning , 1987, AAAI 1987.

[6]  Lambèr M. M. Royakkers,et al.  Collective commitment and obligation , 1998 .

[7]  Bernard Williams,et al.  Problems of the self : philosophical papers, 1956-1972 , 1973 .

[8]  Diderik Batens,et al.  A survey of inconsistency-adaptive logics , 2000 .

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

[10]  Dov M. Gabbay,et al.  Handbook of Philosophical Logic , 2002 .

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

[12]  Anthony Kenny,et al.  Will, freedom, and power , 1975 .

[13]  Barteld P. Kooi,et al.  Moral Conflicts between Groups of Agents , 2008, J. Philos. Log..

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

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

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

[17]  Geoffrey Sayre-Mccord,et al.  Essays on moral realism , 1988 .

[18]  Trevor J. M. Bench-Capon,et al.  On the Instantiation of Knowledge Bases in Abstract Argumentation Frameworks , 2013, CLIMA.

[19]  Yoav Shoham,et al.  A semantical approach to nonmonotonic logics , 1987, LICS 1987.

[20]  Diderik Batens.  Frontiers of Paraconsistent Logic , 2000 .

[21]  A. Montefiore.  NORM AND ACTION , 1964 .

[22]  Anthony Hunter,et al.  Paraconsistent logics , 1998 .

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

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

[25]  Nuel Belnap,et al.  The deliberative stit: A study of action, omission, ability, and obligation , 1995, J. Philos. Log..

[26]  Ruth Barcan Marcus,et al.  Moral Dilemmas and Consistency , 1980 .

[27]  Diderik Batens,et al.  Recent results by the inconsistency-adaptive labourers. , 2007 .

[28]  J. Horty.  Agency and Deontic Logic , 2001 .

[29]  N. Belnap,et al.  Facing the Future: Agents and Choices in Our Indeterminist World , 2001 .

[30]  Bengt Hansson.  Deontic logic and different levels of generality , 2008 .

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

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

[33]  Dov M. Gabbay,et al.  Handbook of paraconsistency , 2007 .

[34]  Diderik Batens,et al.  Towards a Dialogic Interpretation of Dynamic Proofs , 2009 .

[35]  Jörg Hansen.  Conflicting imperatives and dyadic deontic logic , 2005, J. Appl. Log..

[36]  Erik C. W. Krabbe,et al.  Dialogues, Logics and Other Strange Things , 2008 .

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

[38]  Nuel Belnap,et al.  In the realm of agents , 1993, Annals of Mathematics and Artificial Intelligence.

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

[40]  David Ripley,et al.  Paraconsistent Logic , 2015, J. Philos. Log..

[41]  Christian Straßer,et al.  A Paraconsistent Multi-agent Framework for Dealing with Normative Conflicts , 2011, CLIMA.

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

[43]  Lou Goble,et al.  Normative Conflicts and The Logic of ‘Ought’ , 2009 .

[44]  Wei Li,et al.  On logic of paradox , 1995, Proceedings 25th International Symposium on Multiple-Valued Logic.

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

[46]  Jan M. Broersen.  Action negation and alternative reductions for dynamic deontic logics , 2004, J. Appl. Log..

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