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Five faces of minimality

Studia Logica 52 (3):339 - 379 (1993)

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  1. On the Dynamics of Institutional Agreements.Andreas Herzig, Tiago de Lima & Emiliano Lorini - 2009 - Synthese 171 (2):321 - 355.
    In this paper we investigate a logic for modelling individual and collective acceptances that is called acceptance logic. The logic has formulae of the form $A_{Gx} \phi $ reading 'if the agents in the set of agents G identify themselves with institution x then they together accept that φ'. We extend acceptance logic by two kinds of dynamic modal operators. The first kind are public announcements of the form x!ψ, meaning that the agents learn that ψ is the case in (...)
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  • Entitlement and Evidence.Martin Smith - 2013 - Australasian Journal of Philosophy 91 (4):735-753.
    Entitlement is conceived as a kind of positive epistemic status, attaching to certain propositions, that involves no cognitive or intellectual accomplishment on the part of the beneficiary — a status that is in place by default. In this paper I will argue that the notion of entitlement — or something very like it — falls out of an idea that may at first blush seem rather disparate: that the evidential support relation can be understood as a kind of variably strict (...)
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  • Editor's Introduction.André Fuhrmann - 1995 - Notre Dame Journal of Formal Logic 36 (1):1-14.
    The process [by which any individual settles into new opinions] is always the same. The individual has a stock of old opinions already, but he meets a new experience that puts them to a strain…. The result is an inward trouble to which his mind till then had been a stranger, and from which he seeks to escape by modifying his previous mass of opinions. He saves as much of it as he can, for in this matter of belief we (...)
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  • Human Rationality Challenges Universal Logic.Brian R. Gaines - 2010 - Logica Universalis 4 (2):163-205.
    Tarski’s conceptual analysis of the notion of logical consequence is one of the pinnacles of the process of defining the metamathematical foundations of mathematics in the tradition of his predecessors Euclid, Frege, Russell and Hilbert, and his contemporaries Carnap, Gödel, Gentzen and Turing. However, he also notes that in defining the concept of consequence “efforts were made to adhere to the common usage of the language of every day life.” This paper addresses the issue of what relationship Tarski’s analysis, and (...)
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  • (1 other version)Deontic logic.Paul McNamara - 2010 - Stanford Encyclopedia of Philosophy.
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  • (1 other version)Implication with possible exceptions.Herman Jurjus & Harrie de Swart - 2001 - Journal of Symbolic Logic 66 (2):517-535.
    We introduce an implication-with-possible-exceptions and define validity of rules-with-possible-exceptions by means of the topological notion of a full subset. Our implication-with-possible-exceptions characterises the preferential consequence relation as axiomatized by Kraus, Lehmann and Magidor [Kraus, Lehmann, and Magidor, 1990]. The resulting inference relation is non-monotonic. On the other hand, modus ponens and the rule of monotony, as well as all other laws of classical propositional logic, are valid-up-to-possible exceptions. As a consequence, the rules of classical propositional logic do not determine the (...)
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  • Reasoning about general preference relations.Davide Grossi, Wiebe van der Hoek & Louwe B. Kuijer - 2022 - Artificial Intelligence 313 (C):103793.
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  • Epistemology Normalized.Jeremy Goodman & Bernhard Salow - 2023 - Philosophical Review 132 (1):89-145.
    We offer a general framework for theorizing about the structure of knowledge and belief in terms of the comparative normality of situations compatible with one’s evidence. The guiding idea is that, if a possibility is sufficiently less normal than one’s actual situation, then one can know that that possibility does not obtain. This explains how people can have inductive knowledge that goes beyond what is strictly entailed by their evidence. We motivate the framework by showing how it illuminates knowledge about (...)
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  • The cost of consistency: information economy in Paraconsistent Belief Revision.Rafael Testa - 2015 - South American Journal of Logic 1 (2):461-480.
    By Belief Revision it is understood a system that logically explains the rational process of changing beliefs by taking into account a new piece of information. The most influential approach in this field of study, the AGM system, proposed by Alchourrón, Gärdenfors, and Makinson, postulates rationality criteria for different types of belief change. In this paper I shall assess the relationship between those criteria and argue for an opposition between the principles of Information Economy and Consistency. Furthermore, I shall argue (...)
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  • Introduction to: Norms, Logics and Information Systems: New Studies on Deontic Logic and Computer Science.Paul McNamara & Henry Prakken - 1999 - In Henry Prakken & Paul McNamara (eds.), Norms, Logics and Information Systems: New Studies on Deontic Logic and Computer Science. Amsterdam/Oxford/Tokyo/Washington DC: IOS Press. pp. 1-14.
    (See also the separate entry for the volume itself.) This introduction has three parts. The first providing an overview of some main lines of research in deontic logic: the emergence of SDL, Chisholm's paradox and the development of dyadic deontic logics, various other puzzles/challenges and areas of development, along with philosophical applications. The second part focus on some actual and potential fruitful interactions between deontic logic, computer science and artificial intelligence. These include applications of deontic logic to AI knowledge representation (...)
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  • Priority Structures in Deontic Logic.Johan van Benthem, Davide Grossi & Fenrong Liu - 2014 - Theoria 80 (2):116-152.
    This article proposes a systematic application of recent developments in the logic of preference to a number of topics in deontic logic. The key junction is the well‐known Hansson conditional for dyadic obligations. These conditionals are generalized by pairing them with reasoning about syntactic priority structures. The resulting two‐level approach to obligations is tested first against standard scenarios of contrary‐to‐duty obligations, leading also to a generalization for the Kanger‐Anderson reduction of deontic logic. Next, the priority framework is applied to model (...)
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  • HYPE: A System of Hyperintensional Logic.Hannes Leitgeb - 2019 - Journal of Philosophical Logic 48 (2):305-405.
    This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the (...)
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  • Commitment and states of mind with mood and modality.Alex Silk - 2018 - Natural Language Semantics 26 (2):125-166.
    This paper develops an account of mood selection with attitude predicates in French. I start by examining the “contextual commitment” account of mood developed by Portner and Rubinstein Proceedings of SALT 22, CLC Publications, Ithaca, NY, pp 461–487, 2012). A key innovation of Portner and Rubinstein’s account is to treat mood selection as fundamentally depending on a relation between individuals’ attitudes and the predicate’s modal backgrounds. I raise challenges for P&R’s qualitative analysis of contextual commitment and explanations of mood selection. (...)
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  • Weak and Strong Necessity Modals: On Linguistic Means of Expressing "A Primitive Concept OUGHT".Alex Silk - 2021 - In Billy Dunaway & David Plunkett (eds.), Meaning, Decision, and Norms: Themes From the Work of Allan Gibbard. Ann Arbor, Michigan: Maize Books. pp. 203-245.
    This paper develops an account of the meaning of `ought', and the distinction between weak necessity modals (`ought', `should') and strong necessity modals (`must', `have to'). I argue that there is nothing specially ``strong'' about strong necessity modals per se: uses of `Must p' predicate the (deontic/epistemic/etc.) necessity of the prejacent p of the actual world (evaluation world). The apparent ``weakness'' of weak necessity modals derives from their bracketing whether the necessity of the prejacent is verified in the actual world. (...)
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  • (1 other version)Deontic Logic.Paul McNamara - 2006 - In Dov Gabbay & John Woods (eds.), The Handbook of the History of Logic, vol. 7: Logic and the Modalities in the Twentieth Century. Elsevier Press. pp. 197-288.
    Overview of fundamental work in deontic logic.
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  • The algebraic face of minimality.Frank Wolter - 1998 - Logic and Logical Philosophy 6:225.
    Operators which map subsets of a given set to the set of their minimal elements with respect to some relation R form the basis of a semanticapproach in non-monotonic logic, belief revision, conditional logic and updating. In this paper we investigate operators of this type from an algebraicviewpoint. A representation theorem is proved and various properties of theresulting algebras are investigated. It is shown that they behave quite differently from known algebras related to logics, e.g. modal algebras and Heytingalgebras.
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  • (1 other version)Implication with Possible Exceptions.Herman Jurjus & Harrie de Swart - 2001 - Journal of Symbolic Logic 66 (2):517 - 535.
    We introduce an implication-with-possible-exceptions and define validity of rules-with-possible-exceptions by means of the topological notion of a full subset. Our implication-with-possible-exceptions characterises the preferential consequence relation as axiomatized by Kraus, Lehmann and Magidor [Kraus, Lehmann, and Magidor, 1990]. The resulting inference relation is non-monotonic. On the other hand, modus ponens and the rule of monotony, as well as all other laws of classical propositional logic, are valid-up-to-possible exceptions. As a consequence, the rules of classical propositional logic do not determine the (...)
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  • From KLM-style conditionals to defeasible modalities, and back.Katarina Britz & Ivan Varzinczak - 2018 - Journal of Applied Non-Classical Logics 28 (1):92-121.
    We investigate an aspect of defeasibility that has somewhat been overlooked by the non-monotonic reasoning community, namely that of defeasible modes of reasoning. These aim to formalise defeasibility of the traditional notion of necessity in modal logic, in particular of its different readings as action, knowledge and others in specific contexts, rather than defeasibility of conditional forms. Building on an extension of the preferential approach to modal logics, we introduce new modal osperators with which to formalise the notion of defeasible (...)
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  • Speed Up the Conception of Logical Systems with Test-Driven Development.Mathieu Vidal - 2014 - Journal of Logic, Language and Information 23 (1):83-103.
    In this paper, I stress the utility of employing test-driven development (TDD) for conceiving logical systems. TDD, originally invented in the context of Extreme Programming, is a methodology widely used by software engineers to conceive and develop programs. Its main principle is to design the tests of the expected properties of the system before the development phase. I argue that this methodology is especially convenient in conceiving applied logics. Indeed, this technique is efficient with most decidable logics having a software (...)
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  • Completeness and incompleteness for plausibility logic.Karl Schlechta - 1996 - Journal of Logic, Language and Information 5 (2):177-192.
    Plausibility Logic was introduced by Daniel Lehmann. We show—among some other results—completeness of a subset of Plausibility Logic for Preferential Models, and incompleteness of full Plausibility Logic for smooth Preferential Models.
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  • Reasoning about action and change.Helmut Prendinger & Gerhard Schurz - 1996 - Journal of Logic, Language and Information 5 (2):209-245.
    Reasoning about change is a central issue in research on human and robot planning. We study an approach to reasoning about action and change in a dynamic logic setting and provide a solution to problems which are related to the Frame problem. Unlike most work on the frame problem the logic described in this paper is monotonic. It (implicitly) allows for the occurrence of actions of multiple agents by introducing non-stationary notions of waiting and test. The need to state a (...)
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  • Revision, defeasible conditionals and non-monotonic inference for abstract dialectical frameworks.Jesse Heyninck, Gabriele Kern-Isberner, Tjitze Rienstra, Kenneth Skiba & Matthias Thimm - 2023 - Artificial Intelligence 317 (C):103876.
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  • Introduction to Sten Lindström's “A semantic approach to nonmonotonic reasoning: Inference operations and choice”.Hans Rott - 2022 - Theoria 88 (3):491-493.
    Among the most important of Sten Lindström’s achievements in philosophy and logic is that he was the first researcher to realise that the theory of rational choice can be brought to bear in the domain of logic and reasoning. The new conception was that a sentence α is a consequence of a set of sentences Γ just in case α is true in all selected ("best", "most plausible") possible worlds in which all sentences in Γ are true (rather than in (...)
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  • Chaos: The Reason for Structural Causation.Hans Rott - unknown
    The paper attempts to reconcile two very different approaches to the concept of causation. In the original form, it is the opposition found in Laplace between his doctrine of constant and variable causes on the one hand and his mechanistic determinism on the other. This tension was described clearly only by Maxwell who stressed the contrast between the statistical and the dynamical method (calling the latter also the historical or strictly kinetic method). A similar dichotomy surfaces in the work of (...)
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  • Violation games: a new foundation for deontic logic ★.Leendert van der Torre - 2010 - Journal of Applied Non-Classical Logics 20 (4):457-477.
    In this paper I propose violation games as the basis of formal logics to represent and reason about norms, i.e. as the foundation of deontic logic. Deontic logic is an applied non-classical logic reflecting a way in which we conceptualize normative reasoning. By introducing violation games as a fundamental principle of deontic logic, I am introducing a new way of looking at familiar problems in normative reasoning, with the aim of introducing a new approach for handling norms in intelligent systems.
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  • Abductive logics in a belief revision framework.Bernard Walliser, Denis Zwirn & Hervé Zwirn - 2004 - Journal of Logic, Language and Information 14 (1):87-117.
    Abduction was first introduced in the epistemological context of scientific discovery. It was more recently analyzed in artificial intelligence, especially with respect to diagnosis analysis or ordinary reasoning. These two fields share a common view of abduction as a general process of hypotheses formation. More precisely, abduction is conceived as a kind of reverse explanation where a hypothesis H can be abduced from events E if H is a good explanation of E. The paper surveys four known schemes for abduction (...)
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  • Contrary-to-duty obligations.Henry Prakken & Marek Sergot - 1996 - Studia Logica 57 (1):91 - 115.
    We investigate under what conditions contrary-to-duty (CTD) structures lacking temporal and action elements can be given a coherent reading. We argue, contrary to some recent proposals, that CTD is not an instance of defeasible reasoning, and that methods of nonmonotonic logics are inadequate since they are unable to distinguish between defeasibility and violation of primary obligations. We propose a semantic framework based on the idea that primary and CTD obligations are obligations of different kinds: a CTD obligation pertains to, or (...)
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  • Preferences and explanations.Ramón Pino-Pérez & Carlos Uzcátegui - 2003 - Artificial Intelligence 149 (1):1-30.
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  • On Some Weakened Forms of Transitivity in the Logic of Conditional Obligation.Xavier Parent - 2024 - Journal of Philosophical Logic 53 (3):721-760.
    This paper examines the logic of conditional obligation, which originates from the works of Hansson, Lewis, and others. Some weakened forms of transitivity of the betterness relation are studied. These are quasi-transitivity, Suzumura consistency, acyclicity and the interval order condition. The first three do not change the logic. The axiomatic system is the same whether or not they are introduced. This holds true under a rule of interpretation in terms of maximality and strong maximality. The interval order condition gives rise (...)
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  • Logic and Probability: Reasoning in Uncertain Environments – Introduction to the Special Issue.Matthias Unterhuber & Gerhard Schurz - 2014 - Studia Logica 102 (4):663-671.
    The current special issue focuses on logical and probabilistic approaches to reasoning in uncertain environments, both from a formal, conceptual and argumentative perspective as well as an empirical point of view. In the present introduction we give an overview of the types of problems addressed by the individual contributions of the special issue, based on fundamental distinctions employed in this area. We furthermore describe some of the general features of the special issue.
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  • Why was Alchourrón afraid of snakes?Juliano S. A. Maranhão - 2006 - Análisis Filosófico 26 (1):62-92.
    In the last papers published by Alchourrón, he attacked non-monotonic logics, which he considered philosophically unsound for the representation of defeasible reasoning. Instead of a non-monotonic consequence relation, he proposed a formal representation of defeasibility based on an AGM-like revision of implicit assumptions connected to the premises. Given that this is a procedure to generate non-monotonic logics, it is not clear, from a mathematical standpoint, why he was so suspicious of such logics. In the present paper we try to answer (...)
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  • Adaptive Logic as a Modal Logic.Patrick Allo - 2013 - Studia Logica 101 (5):933-958.
    Modal logics have in the past been used as a unifying framework for the minimality semantics used in defeasible inference, conditional logic, and belief revision. The main aim of the present paper is to add adaptive logics, a general framework for a wide range of defeasible reasoning forms developed by Diderik Batens and his co-workers, to the growing list of formalisms that can be studied with the tools and methods of contemporary modal logic. By characterising the class of abnormality models, (...)
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  • Two approaches to the formalisation of defeasible deontic reasoning.Henry Prakken - 1996 - Studia Logica 57 (1):73 - 90.
    This paper compares two ways of formalising defeasible deontic reasoning, both based on the view that the issues of conflicting obligations and moral dilemmas should be dealt with from the perspective of nonmonotonic reasoning. The first way is developing a special nonmonotonic logic for deontic statements. This method turns out to have some limitations, for which reason another approach is recommended, viz. combining an already existing nonmonotonic logic with a deontic logic. As an example of this method the language of (...)
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  • A Complete Axiom Set For Hansson's Deontic Logic Dsdl2.Xavier Parent - 2010 - Logic Journal of the IGPL 18 (3):422-429.
    The main contribution of this paper is a completeness result for an axiomatization of Hansson [13]'s deontic system DSDL2, whose semantics involves a non-necessarily transitive betterness relation. Reference is made to a deductive system put forth by Åqvist [2, 3].
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  • Modellings for belief change: Prioritization and entrenchment.Hans Rott - 1992 - Theoria 58 (1):21-57.
    We distinguish the set of explicit beliefs of a reasoner, his "belief base", from the beliefs that are merely implicit. Syntax-based belief change governed by the structure of the belief base and the ranking ("prioritization") of its elements is reconstructed with the help of an epistemic entrenchment relation in the style of Gärdenfors and Makinson. Though priorities are essentially different from entrenchments, distinguished relations of epistemic entrenchment may be obtained from prioritized belief bases by a number of different constructions. An (...)
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  • New techniques and completeness results for preferential structures.Karl Schlechta - 2000 - Journal of Symbolic Logic 65 (2):719-746.
    Preferential structures are probably the best examined semantics for nonmonotonic and deontic logics; in a wider sense, they also provide semantical approaches to theory revision and update, and other fields where a preference relation between models is a natural approach. They have been widely used to differentiate the various systems of such logics, and their construction is one of the main subjects in the formal investigation of these logics. We introduce new techniques to construct preferential structures for completeness proofs. Since (...)
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  • Maximality vs. Optimality in Dyadic Deontic Logic.Xavier Parent - 2014 - Journal of Philosophical Logic 43 (6):1101-1128.
    This paper reports completeness results for dyadic deontic logics in the tradition of Hansson’s systems. There are two ways to understand the core notion of best antecedent-worlds, which underpins such systems. One is in terms of maximality, and the other in terms of optimality. Depending on the choice being made, one gets different evaluation rules for the deontic modalities, but also different versions of the so-called limit assumption. Four of them are disentangled, and compared. The main observation of this paper (...)
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  • (1 other version)Can Bayes' Rule be Justified by Cognitive Rationality Principles?Walliser Bernard & Zwirn Denis - 2002 - Theory and Decision 53 (2):95-135.
    The justification of Bayes' rule by cognitive rationality principles is undertaken by extending the propositional axiom systems usually proposed in two contexts of belief change: revising and updating. Probabilistic belief change axioms are introduced, either by direct transcription of the set-theoretic ones, or in a stronger way but nevertheless in the spirit of the underlying propositional principles. Weak revising axioms are shown to be satisfied by a General Conditioning rule, extending Bayes' rule but also compatible with others, and weak updating (...)
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  • Local and global metrics for the semantics of counterfactual conditionals.Karl Schlechta & David Makinson - 1994 - Journal of Applied Non-Classical Logics 4 (2):129-140.
    No aConsiders the question of how far the different ‘closeness’ relations, indexed by worlds, in a given model for counterfactual conditionals may be derived from a common source. Counterbalancing some well-known negative observations, we show that there is also a strong positive answer.
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  • Preferential Accessibility and Preferred Worlds.Katarina Britz & Ivan Varzinczak - 2018 - Journal of Logic, Language and Information 27 (2):133-155.
    Modal accounts of normality in non-monotonic reasoning traditionally have an underlying semantics based on a notion of preference amongst worlds. In this paper, we motivate and investigate an alternative semantics, based on ordered accessibility relations in Kripke frames. The underlying intuition is that some world tuples may be seen as more normal, while others may be seen as more exceptional. We show that this delivers an elegant and intuitive semantic construction, which gives a new perspective on defeasible necessity. Technically, the (...)
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  • Blueprint for a dynamic deontic logic.Krister Segerberg - 2009 - Journal of Applied Logic 7 (4):388-402.
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  • Reactive Kripke models and contrary to duty obligations. Part A: Semantics.Dov M. Gabbay - 2013 - Journal of Applied Logic 11 (1):103-136.
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  • Gricean Belief Change.James P. Delgrande, Abhaya C. Nayak & Maurice Pagnucco - 2005 - Studia Logica 79 (1):97-113.
    One of the standard principles of rationality guiding traditional accounts of belief change is the principle of minimal change: a reasoner's belief corpus should be modified in a minimal fashion when assimilating new information. This rationality principle has stood belief change in good stead. However, it does not deal properly with all belief change scenarios. We introduce a novel account of belief change motivated by one of Grice's maxims of conversational implicature: the reasoner's belief corpus is modified in a minimal (...)
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  • Conditional normative reasoning as a fragment of HOL.Xavier Parent & Christoph Benzmüller - 2024 - Journal of Applied Non-Classical Logics 34 (4):561-592.
    We report on the mechanisation of (preference-based) conditional normative reasoning. Our focus is on Åqvist's system E for conditional obligation, and its extensions. Our mechanisation is achieved via a shallow semantical embedding in Isabelle/HOL. We consider two possible uses of the framework. The first one is as a tool for meta-reasoning about the considered logic. We employ it for the automated verification of deontic correspondences (broadly conceived) and related matters, analogous to what has been previously achieved for the modal logic (...)
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  • Constructive Modelings for Theory Change.Pavlos Peppas & Mary-Anne Williams - 1995 - Notre Dame Journal of Formal Logic 36 (1):120-133.
    Alchourrón, Gärdenfors and Makinson have developed and investigated a set of rationality postulates which appear to capture much of what is required of any rational system of theory revision. This set of postulates describes a class of revision functions, however it does not provide a constructive way of defining such a function. There are two principal constructions of revision functions, namely an epistemic entrenchment and a system of spheres. We refer to their approach as the AGM paradigm. We provide a (...)
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  • Remedial interchange, contrary-to-duty obligation and commutation.Xavier Parent - 2003 - Journal of Applied Non-Classical Logics 13 (3):345-375.
    This paper discusses the relation between deontic logic and the study of conversational interactions. Special attention is given to the notion of remedial interchange as analysed by sociologists and linguistic pragmaticians. This notion is close to the one of contrary-to-duty (reparational) obligation, which deontic logicians have been studying in its own right. The present article also investigates the question of whether some of the aspects of conversational interactions can fruitfully be described by using formal tools originally developed in the study (...)
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  • Priority Structures in Deontic Logic.Johan Benthem, Davide Grossi & Fenrong Liu - 2013 - Theoria 80 (2):116-152.
    This article proposes a systematic application of recent developments in the logic of preference to a number of topics in deontic logic. The key junction is the well-known Hansson conditional for dyadic obligations. These conditionals are generalized by pairing them with reasoning about syntactic priority structures. The resulting two-level approach to obligations is tested first against standard scenarios of contrary-to-duty obligations, leading also to a generalization for the Kanger-Anderson reduction of deontic logic. Next, the priority framework is applied to model (...)
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  • (1 other version)Can Bayes' Rule be Justified by Cognitive Rationality Principles?Bernard Walliser & Denis Zwirn - 2002 - Theory and Decision 53 (2):95-135.
    The justification of Bayes' rule by cognitive rationality principles is undertaken by extending the propositional axiom systems usually proposed in two contexts of belief change: revising and updating. Probabilistic belief change axioms are introduced, either by direct transcription of the set-theoretic ones, or in a stronger way but nevertheless in the spirit of the underlying propositional principles. Weak revising axioms are shown to be satisfied by a General Conditioning rule, extending Bayes' rule but also compatible with others, and weak updating (...)
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  • Conditional logic of actions and causation.Laura Giordano & Camilla Schwind - 2004 - Artificial Intelligence 157 (1-2):239-279.
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  • Boolean algebras of conditionals, probability and logic.Tommaso Flaminio, Lluis Godo & Hykel Hosni - 2020 - Artificial Intelligence 286 (C):103347.
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