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  1. Five faces of minimality.David Makinson - 1993 - Studia Logica 52 (3):339 - 379.
    We discuss similarities and residual differences, within the general semantic framework of minimality, between defeasible inference, belief revision, counterfactual conditionals, updating — and also conditional obligation in deontic logic. Our purpose is not to establish new results, but to bring together existing material to form a clear overall picture.
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  • Nonmonotonic probabilistic reasoning under variable-strength inheritance with overriding.Thomas Lukasiewicz - 2005 - Synthese 146 (1-2):153 - 169.
    We present new probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment, called Zλ- and lexλ-entailment, which are parameterized through a value λ ∈ [0,1] that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of λ = 0 and λ = 1, the notions of Zλ- and lexλ-entailment coincide with probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment that have been recently introduced by the author. We show (...)
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  • Deontic logics for prioritized imperatives.Jörg Hansen - 2006 - Artificial Intelligence and Law 14 (1-2):1-34.
    When a conflict of duties arises, a resolution is often sought by use of an ordering of priority or importance. This paper examines how such a conflict resolution works, compares mechanisms that have been proposed in the literature, and gives preference to one developed by Brewka and Nebel. I distinguish between two cases – that some conflicts may remain unresolved, and that a priority ordering can be determined that resolves all – and provide semantics and axiomatic systems for accordingly defined (...)
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  • A note on the rational closure of knowledge bases with both positive and negative knowledge.R. Booth & J. B. Paris - 1998 - Journal of Logic, Language and Information 7 (2):165-190.
    The notion of the rational closure of a positive knowledge base K of conditional assertions θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} |∼ φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} (standing for if θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} then normally φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document}) was first introduced by Lehmann (1989) and developed by Lehmann and Magidor (...)
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  • Defaults as restrictions on classical Hilbert-style proofs.Gianni Amati, Luigia Carlucci Aiello & Fiora Pirri - 1994 - Journal of Logic, Language and Information 3 (4):303-326.
    Since the earliest formalisation of default logic by Reiter many contributions to this appealing approach to nonmonotonic reasoning have been given. The different formalisations are here presented in a general framework that gathers the basic notions, concepts and constructions underlying default logic. Our view is to interpret defaults as special rules that impose a restriction on the juxtaposition of monotonic Hubert-style proofs of a given logicL. We propose to describe default logic as a logic where the juxtaposition of default proofs (...)
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  • Proof with and without probabilities.Bart Verheij - 2017 - Artificial Intelligence and Law 25 (1):127-154.
    Evidential reasoning is hard, and errors can lead to miscarriages of justice with serious consequences. Analytic methods for the correct handling of evidence come in different styles, typically focusing on one of three tools: arguments, scenarios or probabilities. Recent research used Bayesian networks for connecting arguments, scenarios, and probabilities. Well-known issues with Bayesian networks were encountered: More numbers are needed than are available, and there is a risk of misinterpretation of the graph underlying the Bayesian network, for instance as a (...)
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  • Distance-based non-deterministic semantics for reasoning with uncertainty.Ofer Arieli & Anna Zamansky - 2009 - Logic Journal of the IGPL 17 (4):325-350.
    Non-deterministic matrices, a natural generalization of many-valued matrices, are semantic structures in which the value assigned to a complex formula may be chosen non-deterministically from a given set of options. We show that by combining non-deterministic matrices and distance-based considerations, one obtains a family of logics that are useful for reasoning with uncertainty. These logics are a conservative extension of those that are obtained by standard distance-based semantics, and so usual distance-based methods are easily simulated within our framework. We investigate (...)
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  • Jumping to Conclusions.Bart Verheij - 2012 - In Luis Farinas del Cerro, Andreas Herzig & Jerome Mengin (eds.), Logics in Artificial Intelligence. Springer. pp. 411--423.
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  • Revocable Belief Revision.Hans van Ditmarsch - 2013 - Studia Logica 101 (6):1185-1214.
    Krister Segerberg proposed irrevocable belief revision, to be contrasted with standard belief revision, in a setting wherein belief of propositional formulas is modelled explicitly. This suggests that in standard belief revision is revocable: one should be able to unmake (‘revoke’) the fresh belief in the revision formula, given yet further information that contradicts it. In a dynamic epistemic logical setting for belief revision, for multiple agents, we investigate what the requirements are for revocable belief revision. By this we not merely (...)
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  • A General Family of Preferential Belief Removal Operators.Richard Booth, Thomas Meyer & Chattrakul Sombattheera - 2012 - Journal of Philosophical Logic 41 (4):711 - 733.
    Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in Booth et al. (Artif Intell 174:1339-1368, 2010). However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of Booth et al. (Artif Intell 174: 1339-1368, 2010) (...)
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  • Reactive preferential structures and nonmonotonic consequence.Dov M. Gabbay & Karl Schlechta - 2009 - Review of Symbolic Logic 2 (2):414-450.
    We introduce Information Bearing Relation Systems (IBRS) as an abstraction of many logical systems. These are networks with arrows recursively leading to other arrows etc. We then define a general semantics for IBRS, and show that a special case of IBRS generalizes in a very natural way preferential semantics and solves open representation problems for weak logical systems. This is possible, as we can the strong coherence properties of preferential structures by higher arrows, that is, arrows, which do not go (...)
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  • Cumulativity without closure of the domain under finite unions.Dov M. Gabbay & Karl Schlechta - 2008 - Review of Symbolic Logic 1 (3):372-392.
    For nonmonotonic logics, Cumulativity is an important logical rule. We show here that Cumulativity fans out into an infinity of different conditions, if the domain is not closed under finite unions.
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  • Distance semantics for belief revision.Daniel Lehmann, Menachem Magidor & Karl Schlechta - 2001 - Journal of Symbolic Logic 66 (1):295-317.
    A vast and interesting family of natural semantics for belief revision is defined. Suppose one is given a distance d between any two models. One may then define the revision of a theory K by a formula α as the theory defined by the set of all those models of α that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates (...)
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  • Possibilistic reasoning—a mini-survey and uniform semantics.Churn-Jung Liau & Bertrand I.-Peng Lin - 1996 - Artificial Intelligence 88 (1-2):163-193.
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  • On the Transitivity of Logical Consequence without Assuming Monotonicity.Lin Chen & Xuefeng Wen - forthcoming - Logica Universalis:1-16.
    We generalize Ripley’s results on the transitivity of consequence relation, without assuming a logic to be monotonic. Following Gabbay, we assume nonmonotonic consequence relation to be inclusive and cautious monotonic, and figure out the implications between different forms of transitivity of logical consequence. Weaker frameworks without inclusiveness or cautious monotonicity are also discussed. The paper may provide basis for the study of both non-transitive logics and nonmonotonic ones.
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  • Selecting accepted assertions in partially ordered inconsistent DL-Lite knowledge bases.Sihem Belabbes & Salem Benferhat - 2023 - Journal of Applied Non-Classical Logics 33 (3-4):561-581.
    1. Real-world applications, such as monitoring urban wastewater networks, commonly process large volumes of multi-source, heterogeneous data to support reasoning, query answering and decision-makin...
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  • When is argumentation deductive?Henry Prakken - 2023 - Journal of Applied Non-Classical Logics 33 (3-4):212-223.
    1. In May 2013 I had an email exchange with Philippe Besnard, continued in September that year, on his paper with Amgoud and Besnard (2013) and its relevance for the ASPIC+ framework (Modgil & Prak...
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  • Towards a logic for ‘because’.Eric Raidl & Hans Rott - forthcoming - Philosophical Studies:1-31.
    This paper explores the connective ‘because’, based on the idea that ‘CbecauseA’ implies the acceptance/truth of the antecedentAas well as of the consequentC, and additionally that the antecedent makes a difference for the consequent. To capture this idea of difference-making a ‘relevantized’ version of the Ramsey Test for conditionals is employed that takes the antecedent to be relevant to the consequent in the following sense: a conditional is true/accepted in a state$$\sigma $$σjust in case (i) the consequent is true/accepted when$$\sigma (...)
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  • A postulate-driven study of logical argumentation.Ofer Arieli, AnneMarie Borg & Christian Straßer - 2023 - Artificial Intelligence 322 (C):103966.
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  • Defeasible linear temporal logic.Anasse Chafik, Fahima Cheikh-Alili, Jean-François Condotta & Ivan Varzinczak - 2023 - Journal of Applied Non-Classical Logics 33 (1):1-51.
    After the seminal work of Kraus, Lehmann and Magidor (formally known as the KLM approach) on conditionals and preferential models, many aspects of defeasibility in more complex formalisms have been studied in recent years. Examples of these aspects are the notion of typicality in description logic and defeasible necessity in modal logic. We discuss a new aspect of defeasibility that can be expressed in the case of temporal logic, which is the normality in an execution. In this contribution, we take (...)
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  • Metasequents and Tetravaluations.Rohan French - 2022 - Journal of Philosophical Logic 51 (6):1453-1476.
    In this paper we treat metasequents—objects which stand to sequents as sequents stand to formulas—as first class logical citizens. To this end we provide a metasequent calculus, a sequent calculus which allows us to directly manipulate metasequents. We show that the various metasequent calculi we consider are sound and complete w.r.t. appropriate classes of tetravaluations where validity is understood locally. Finally we use our metasequent calculus to give direct syntactic proofs of various collapse results, closing a problem left open in (...)
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  • Choice logics and their computational properties.Michael Bernreiter, Jan Maly & Stefan Woltran - 2022 - Artificial Intelligence 311 (C):103755.
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  • An abstract, logical approach to characterizing strong equivalence in non-monotonic knowledge representation formalisms.Ringo Baumann & Hannes Strass - 2022 - Artificial Intelligence 305 (C):103680.
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  • Conceptual Learning and Local Incommensurability: A Dynamic Logic Approach.Corina Strößner - 2022 - Axiomathes 32 (6):1025-1045.
    In recent decades, the logical study of rational belief dynamics has played an increasingly important role in philosophy. However, the dynamics of concepts such as conceptual learning received comparatively little attention within this debate. This is problematic insofar as the occurrence of conceptual change (especially in the sciences) has been an influential argument against a merely logical analysis of beliefs. Especially Kuhn’s ideas about the incommensurability, i.e., untranslatability, of succeeding theories seem to stand in the way of logical reconstruction. This (...)
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  • Properties and interrelationships of skeptical, weakly skeptical, and credulous inference induced by classes of minimal models.Christoph Beierle, Christian Eichhorn, Gabriele Kern-Isberner & Steven Kutsch - 2021 - Artificial Intelligence 297 (C):103489.
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  • Logic of Convex Order.Chenwei Shi & Yang Sun - 2021 - Studia Logica 109 (5):1019-1047.
    Based on a pre-order on a set, we axiomatize the Egli-Milner order on the power set and show how it is related to the Lewis order. Moreover, we consider a strict version of the Egli-Milner order and show how it can be related to the semantics of conditionals based on a priority structure.
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  • On rational entailment for Propositional Typicality Logic.Richard Booth, Giovanni Casini, Thomas Meyer & Ivan Varzinczak - 2019 - Artificial Intelligence 277 (C):103178.
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  • Rational closure for all description logics.P. A. Bonatti - 2019 - Artificial Intelligence 274 (C):197-223.
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  • An axiomatic analysis of structured argumentation with priorities.Phan Minh Dung - 2016 - Artificial Intelligence 231 (C):107-150.
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  • Interpolative and extrapolative reasoning in propositional theories using qualitative knowledge about conceptual spaces.Steven Schockaert & Henri Prade - 2013 - Artificial Intelligence 202 (C):86-131.
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  • A defeasible reasoning model of inductive concept learning from examples and communication.Santiago Ontañón, Pilar Dellunde, Lluís Godo & Enric Plaza - 2012 - Artificial Intelligence 193 (C):129-148.
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  • Preferences in AI: An overview.Carmel Domshlak, Eyke Hüllermeier, Souhila Kaci & Henri Prade - 2011 - Artificial Intelligence 175 (7-8):1037-1052.
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  • Interventions and belief change in possibilistic graphical models.Salem Benferhat - 2010 - Artificial Intelligence 174 (2):177-189.
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  • From the textual description of an accident to its causes.Daniel Kayser & Farid Nouioua - 2009 - Artificial Intelligence 173 (12-13):1154-1193.
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  • Using arguments for making and explaining decisions.Leila Amgoud & Henri Prade - 2009 - Artificial Intelligence 173 (3-4):413-436.
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  • On the notion of concept II.Michael Freund - 2009 - Artificial Intelligence 173 (1):167-179.
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  • Expressive probabilistic description logics.Thomas Lukasiewicz - 2008 - Artificial Intelligence 172 (6-7):852-883.
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  • Weak nonmonotonic probabilistic logics.Thomas Lukasiewicz - 2005 - Artificial Intelligence 168 (1-2):119-161.
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  • Combining probabilistic logic programming with the power of maximum entropy.Gabriele Kern-Isberner & Thomas Lukasiewicz - 2004 - Artificial Intelligence 157 (1-2):139-202.
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  • A nonmonotonic observation logic.Frans Voorbraak - 2004 - Artificial Intelligence 157 (1-2):281-302.
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  • Introduction: Progress in formal commonsense reasoning.Ernest Davis & Leora Morgenstern - 2004 - Artificial Intelligence 153 (1-2):1-12.
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  • Qualitative decision theory with preference relations and comparative uncertainty: An axiomatic approach.Didier Dubois, Hélène Fargier & Patrice Perny - 2003 - Artificial Intelligence 148 (1-2):219-260.
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  • Rationality, transitivity, and contraposition.Michael Freund, Daniel Lehmann & Paul Morris - 1991 - Artificial Intelligence 52 (2):191-203.
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  • A logic for reasoning with inconsistent knowledge.Nico Roos - 1992 - Artificial Intelligence 57 (1):69-103.
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  • Unifying default reasoning and belief revision in a modal framework.Craig Boutilier - 1994 - Artificial Intelligence 68 (1):33-85.
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  • From statistical knowledge bases to degrees of belief.Fahiem Bacchus, Adam J. Grove, Joseph Y. Halpern & Daphne Koller - 1996 - Artificial Intelligence 87 (1-2):75-143.
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  • Reasoning by cases in default logic.Nico Roos - 1998 - Artificial Intelligence 99 (1):165-183.
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  • Probabilistic semantics for Delgrande's conditional logic and a counterexample to his default logic.Gerhard Schurz - 1998 - Artificial Intelligence 102 (1):81-95.
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  • On first-order conditional logics.James P. Delgrande - 1998 - Artificial Intelligence 105 (1-2):105-137.
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  • On the relation between default and modal nonmonotonic reasoning.Alexander Bochman - 1998 - Artificial Intelligence 101 (1-2):1-34.
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