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  1. Free choice reasons.Daniel Bonevac - 2019 - Synthese 196 (2):735-760.
    I extend theories of nonmonotonic reasoning to account for reasons allowing free choice. My approach works with a wide variety of approaches to nonmonotonic reasoning and explains the connection between reasons for kinds of action and reasons for actions or subkinds falling under them. I use an Anderson–Kanger reduction of reason statements, identifying key principles in the logic of reasons.
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  • Bisimulation for Conditional Modalities.A. Baltag & G. Cinà - 2018 - Studia Logica 106 (1):1-33.
    We give a definition of bisimulation for conditional modalities interpreted on selection functions and prove the correspondence between bisimilarity and modal equivalence, generalizing the Hennessy–Milner Theorem to a wide class of conditional operators. We further investigate the operators and semantics to which these results apply. First, we show how to derive a solid notion of bisimulation for conditional belief, behaving as desired both on plausibility models and on evidence models. These novel definitions of bisimulations are exploited in a series of (...)
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  • The Logic of “Most” and “Mostly”.Corina Strößner - 2018 - Axiomathes 28 (1):107-124.
    The paper suggests a modal predicate logic that deals with classical quantification and modalities as well as intermediate operators, like “most” and “mostly”. Following up the theory of generalized quantifiers, we will understand them as two-placed operators and call them determiners. Quantifiers as well as modal operators will be constructed from them. Besides the classical deduction, we discuss a weaker probabilistic inference “therefore, probably” defined by symmetrical probability measures in Carnap’s style. The given probabilistic inference relates intermediate quantification to singular (...)
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  • In All But Finitely Many Possible Worlds: Model-Theoretic Investigations on ‘ Overwhelming Majority ’ Default Conditionals.Costas D. Koutras & Christos Rantsoudis - 2017 - Journal of Logic, Language and Information 26 (2):109-141.
    Defeasible conditionals are statements of the form ‘if A then normally B’. One plausible interpretation introduced in nonmonotonic reasoning dictates that ) is true iff B is true in ‘most’ A-worlds. In this paper, we investigate defeasible conditionals constructed upon a notion of ‘overwhelming majority’, defined as ‘truth in a cofinite subset of \’, the first infinite ordinal. One approach employs the modal logic of the frame \\), used in the temporal logic of discrete linear time. We introduce and investigate (...)
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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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  • Belief Contraction in the Context of the General Theory of Rational Choice.Hans Rott - 1993 - Journal of Symbolic Logic 59 (4):1426-1450.
    This paper reorganizes and further develops the theory of partial meet contraction which was introduced in a classic paper by Alchourron, Gardenfors, and Makinson. Our purpose is threefold. First, we put the theory in a broader perspective by decomposing it into two layers which can respectively be treated by the general theory of choice and preference and elementary model theory. Second, we reprove the two main representation theorems of AGM and present two more representation results for the finite case that (...)
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  • Reward versus risk in uncertain inference: Theorems and simulations.Gerhard Schurz & Paul D. Thorn - 2012 - Review of Symbolic Logic 5 (4):574-612.
    Systems of logico-probabilistic reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systems _O, P_, _Z_, and _QC_. These systems differ in the number of inferences they licence _. LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of drawing more false or uninformative conclusions. In the first part of the paper, we (...)
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  • Probability and Conditionals: Belief Revision and Rational Decision. [REVIEW]Joseph Y. Halpern - 2000 - Philosophical Review 109 (2):277-281.
    This collection of essays is a Festschrift for Ernest W. Adams, and is based on a symposium that was held in his honor in 1993. As the title suggests, most of the essays focus on probability and the logic of conditionals, and the relationship between them; they draw their inspiration from Adams’s seminal work on the subject. As a computer scientist, I was struck by just how much the topics discussed play a major role in much recent work in computer (...)
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  • Probability and Conditionals: Belief Revision and Rational Decision. [REVIEW]Joseph Y. Halpern - 2000 - Philosophical Review 109 (2):277-281.
    This collection of essays is a Festschrift for Ernest W. Adams, and is based on a symposium that was held in his honor in 1993. As the title suggests, most of the essays focus on probability and the logic of conditionals, and the relationship between them; they draw their inspiration from Adams’s seminal work on the subject. As a computer scientist, I was struck by just how much the topics discussed play a major role in much recent work in computer (...)
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  • Reasoning Biases, Non‐Monotonic Logics and Belief Revision.Catarina Dutilh Novaes & Herman Veluwenkamp - 2016 - Theoria 83 (1):29-52.
    A range of formal models of human reasoning have been proposed in a number of fields such as philosophy, logic, artificial intelligence, computer science, psychology, cognitive science, etc.: various logics, probabilistic systems, belief revision systems, neural networks, among others. Now, it seems reasonable to require that formal models of human reasoning be empirically adequate if they are to be viewed as models of the phenomena in question. How are formal models of human reasoning typically put to empirical test? One way (...)
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  • Modelling reasoning processes in natural agents: a partial-worlds-based logical framework for elemental non-monotonic inferences and learning.Christel Grimaud - 2016 - Journal of Applied Non-Classical Logics 26 (4):251-285.
    In this paper we address the modelling of reasoning processes in natural agents. We focus on a very basic kind of non-monotonic inference for which we identify a simple and plausible underlying process, and we develop a family of logical models that allow to match this process. Partial worlds models, as we call them, are a variant of Kraus, Lehmann and Magidor’s cumulative models. We show that the inference relations they induce form a strict subclass of cumulative relations and tackle (...)
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  • Probability and Conditionals: Belief Revision and Rational Decision.Joseph Y. Halpern, Ellery Eells & Brian Skyrms - 2000 - Philosophical Review 109 (2):277.
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  • Believability Relations for Select-Direct Sentential Revision.Li Zhang - 2017 - Studia Logica 105 (1):37-63.
    A set of sentential revision operations can be generated in a select-direct way within a new framework for belief change named descriptor revision firstly introduced in Hansson [8]. In this paper, we adopt another constructive approach to these operations, based on a relation \ on sentences named believability relation. Intuitively, \ means that the subject is at least as prone to believe or accept \ as to believe or accept \. We demonstrate that so called H-believability relations and basic believability (...)
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  • A first-order probabilistic logic with approximate conditional probabilities.N. Ikodinovi, M. Ra Kovi, Z. Markovi & Z. Ognjanovi - 2014 - Logic Journal of the IGPL 22 (4):539-564.
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  • A postulate-based analysis of comparative preference statements.Souhila Kaci & Namrata Patel - 2014 - Journal of Applied Logic 12 (4):501-521.
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  • A deontic logic framework allowing for factual detachment.Christian Straßer - 2011 - Journal of Applied Logic 9 (1):61-80.
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  • Reasoning with prioritized information by iterative aggregation of distance functions.Ofer Arieli - 2008 - Journal of Applied Logic 6 (4):589-605.
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  • Representation theorems for explanatory reasoning based on cumulative models.Arelis Díaz & Carlos Uzcátegui - 2008 - Journal of Applied Logic 6 (4):564-579.
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  • Conflicting imperatives and dyadic deontic logic.Jörg Hansen - 2005 - Journal of Applied Logic 3 (3-4):484-511.
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  • Explaining default intuitions using maximum entropy.Rachel A. Bourne - 2003 - Journal of Applied Logic 1 (3-4):255-271.
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  • System JLZ – rational default reasoning by minimal ranking constructions.Emil Weydert - 2003 - Journal of Applied Logic 1 (3-4):273-308.
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  • A Game Semantics for System P.J. Marti & R. Pinosio - 2016 - Studia Logica 104 (6):1119-1144.
    In this paper we introduce a game semantics for System P, one of the most studied axiomatic systems for non-monotonic reasoning, conditional logic and belief revision. We prove soundness and completeness of the game semantics with respect to the rules of System P, and show that an inference is valid with respect to the game semantics if and only if it is valid with respect to the standard order semantics of System P. Combining these two results leads to a new (...)
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  • Reasoning Processes as Epistemic Dynamics.Olga Pombo - 2015 - Axiomathes 25 (1):41-60.
    This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...)
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  • Adaptive Logic Characterizations of Input/Output Logic.Christian Straßer, Mathieu Beirlaen & Frederik Van De Putte - 2016 - Studia Logica 104 (5):869-916.
    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 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.
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  • A Comment on Work by Booth and Co-authors.Dov M. Gabbay & Karl Schlechta - 2010 - Studia Logica 94 (3):403-432.
    Booth and his co-authors have shown in [2], that many new approaches to theory revision (with fixed K ) can be represented by two relations, , where is a sub-relation of < . They have, however, left open a characterization of the infinite case, which we treat here.
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  • Applied Logic without Psychologism.Gregory Wheeler - 2008 - Studia Logica 88 (1):137-156.
    Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology (...)
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  • The Quantitative/Qualitative Watershed for Rules of Uncertain Inference.James Hawthorne & David Makinson - 2007 - Studia Logica 86 (2):247-297.
    We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness problems; and threshold-sensitive conditions such as `preface' and `lottery' rules.
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  • Rationality and Value: The Epistemological Role of Indeterminate and Agent-dependent Values.Horacio Arló Costa - 2006 - Philosophical Studies 128 (1):7-48.
    An important trend in contemporary epistemology centers on elaborating an old idea of pragmatist pedigree: theory selection (and in general the process of changing view and fixing beliefs) presupposes epistemic values. This article focuses on analyzing the case where epistemic values are indeterminate or when the sources of valuation are multiple (epistemic values like coherence and simplicity need not order options in compatible ways). According to the theory that thus arises epistemic alternatives need not be fully ordered by an underlying (...)
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  • Human Nonmonotonic Reasoning: the Importance of Seeing the Logical Strength of Arguments.Marilyn Ford - 2005 - Synthese 146 (1-2):71-92.
    Three studies of human nonmonotonic reasoning are described. The results show that people find such reasoning quite difficult, although being given problems with known subclass-superclass relationships is helpful. The results also show that recognizing differences in the logical strengths of arguments is important for the nonmonotonic problems studied. For some of these problems, specificity – which is traditionally considered paramount in drawing appropriate conclusions – was irrelevant and so should have lead to a “can’t tell” response; however, people could give (...)
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  • Interpreted Dynamical Systems and Qualitative Laws: from Neural Networks to Evolutionary Systems.Hannes Leitgeb - 2005 - Synthese 146 (1-2):189-202.
    . Interpreted dynamical systems are dynamical systems with an additional interpretation mapping by which propositional formulas are assigned to system states. The dynamics of such systems may be described in terms of qualitative laws for which a satisfaction clause is defined. We show that the systems Cand CL of nonmonotonic logic are adequate with respect to the corresponding description of the classes of interpreted ordered and interpreted hierarchical systems, respectively. Inhibition networks, artificial neural networks, logic programs, and evolutionary systems are (...)
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  • Nonmonotonic Inferences and Neural Networks.Reinhard Blutner - 2004 - Synthese 142 (2):143-174.
    There is a gap between two different modes of computation: the symbolic mode and the subsymbolic (neuron-like) mode. The aim of this paper is to overcome this gap by viewing symbolism as a high-level description of the properties of (a class of) neural networks. Combining methods of algebraic semantics and non-monotonic logic, the possibility of integrating both modes of viewing cognition is demonstrated. The main results are (a) that certain activities of connectionist networks can be interpreted as non-monotonic inferences, and (...)
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  • Iterated Descriptor Revision and the Logic of Ramsey Test Conditionals.Sven Ove Hansson - 2016 - Journal of Philosophical Logic 45 (4):429-450.
    Two of the major problems in AGM-style belief revision, namely the difficulties in accounting for iterated change and for Ramsey test conditionals, have satisfactory solutions in descriptor revision. In descriptor revision, the input is a metalinguistic sentence specifying the success condition of the operation. The choice mechanism selects one of the potential outcomes in which the success condition is satisfied. Iteration of this operation is unproblematic. Ramsey test conditionals can be introduced without giving rise to the paradoxical results that they (...)
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  • Completeness of Åqvist’s Systems E_ and _F.Xavier Parent - 2015 - Review of Symbolic Logic 8 (1):164-177.
    This paper tackles an open problem posed by Åqvist. It is the problem of whether his dyadic deontic systemsEandFare complete with respect to their intended Hanssonian preference-based semantics. It is known that there are two different ways of interpreting what it means for a world to be best or top-ranked among alternatives. This can be understood as saying that it is optimal among them, or maximal among them. First, it is established that, under either the maximality rule or the optimality (...)
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  • Intricate Axioms as Interaction Axioms.Guillaume Aucher - 2015 - Studia Logica 103 (5):1035-1062.
    In epistemic logic, some axioms dealing with the notion of knowledge are rather convoluted and difficult to interpret intuitively, even though some of them, such as the axioms.2 and.3, are considered to be key axioms by some epistemic logicians. We show that they can be characterized in terms of understandable interaction axioms relating knowledge and belief or knowledge and conditional belief. In order to show it, we first sketch a theory dealing with the characterization of axioms in terms of interaction (...)
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  • O is Not Enough.J. B. Paris - 2009 - Review of Symbolic Logic 2 (2):298.
    We examine the closure conditions of the probabilistic consequence relation of Hawthorne and Makinson, specifically the outstanding question of completeness in terms of Horn rules, of their proposed (finite) set of rules O. We show that on the contrary no such finite set of Horn rules exists, though we are able to specify an infinite set which is complete.
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  • Defeasible inheritance systems and reactive diagrams.Dov Gabbay - 2008 - Logic Journal of the IGPL 17 (1):1-54.
    Inheritance diagrams are directed acyclic graphs with two types of connections between nodes: x → y and x ↛ y . Given a diagram D, one can ask the formal question of “is there a valid path between node x and node y?” Depending on the existence of a valid path we can answer the question “x is a y” or “x is not a y”. The answer to the above question is determined through a complex inductive algorithm on paths (...)
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  • A Defeasible Logic For Modelling Policy-based Intentions And Motivational Attitudes.Guido Governatori, Vineet Padmanabhan, Antonio Rotolo & Abdul Sattar - 2009 - Logic Journal of the IGPL 17 (3):227-265.
    In this paper we show how defeasible logic could formally account for the non-monotonic properties involved in motivational attitudes like intention and obligation. Usually, normal modal operators are used to represent such attitudes wherein classical logical consequence and the rule of necessitation comes into play, i.e., ⊢A/⊢ □A, that is from ⊢A derive ⊢ □A. This means that such formalisms are affected by the Logical Omniscience problem. We show that policy-based intentions exhibit non-monotonic behaviour which could be captured through a (...)
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  • A First-order Conditional Probability Logic.Miloš Milošević & Zoran Ognjanović - 2012 - Logic Journal of the IGPL 20 (1):235-253.
    In this article, we present the probability logic LFOCP which is suitable to formalize statements about conditional probabilities of first order formulas. The logical language contains formulas such as CP≥s and CP≤s with the intended meaning ‘the conditional probability of ϕ given θ is at least s’ and ‘at most s’, respectively, where ϕ and θ are first-order formulas. We introduce a class of first order Kripke-like models that combine properties of the usual Kripke models and finitely additive probabilities. We (...)
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  • Pragmatic Interpretations of Vague Expressions: Strongest Meaning and Nonmonotonic Consequence.Pablo Cobreros, Paul Egré, Dave Ripley & Robert van Rooij - 2015 - Journal of Philosophical Logic 44 (4):375-393.
    Recent experiments have shown that naive speakers find borderline contradictions involving vague predicates acceptable. In Cobreros et al. we proposed a pragmatic explanation of the acceptability of borderline contradictions, building on a three-valued semantics. In a reply, Alxatib et al. show, however, that the pragmatic account predicts the wrong interpretations for some examples involving disjunction, and propose as a remedy a semantic analysis instead, based on fuzzy logic. In this paper we provide an explicit global pragmatic interpretation rule, based on (...)
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  • Nonmonotonic reasoning: from finitary relations to infinitary inference operations.Michael Freund & Daniel Lehmann - 1994 - Studia Logica 53 (2):161-201.
    A. Tarski [22] proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and consider more general operations, inference operations. These operations describe the nonmonotonic logics both humans and machines seem to be using when infering defeasible information from incomplete knowledge. We single out a number of interesting families of inference operations. This study of infinitary inference operations (...)
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  • Non-additive degrees of belief.Rolf Haenni - 2009 - In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of belief. London: Springer. pp. 121--159.
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  • The hypothetico-probabilistic (HP-) method as a concretization of the HD-method.T. Kuipers - 2007 - In Sami Pihlström, Panu Raatikainen & Matti Sintonen (eds.), Approaching truth: essays in honour of Ilkka Niiniluoto. London: College Publications. pp. 179--207.
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  • Reasoning with different levels of uncertainty.Ofer Arieli - 2003 - Journal of Applied Non-Classical Logics 13 (3):317-343.
    We introduce a family of preferential logics that are useful for handling information with different levels of uncertainty. The corresponding consequence relations are nonmonotonic, paraconsistent, adaptive, and rational. It is also shown that the formalisms in this family can be embedded in corresponding four-valued logics with at most three uncertainty levels, and that reasoning with these logics can be simulated by algorithms for processing circumscriptive theories, such as DLS and SCAN.
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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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  • The lexicographic closure as a revision process.Richard Booth - 2001 - Journal of Applied Non-Classical Logics 11 (1):35-58.
    The connections between nonmonotonic reasoning and belief revision are well-known. A central problem in the area of nonmonotonic reasoning is the problem of default entailment, i.e., when should an item of default information representing “if θ is true then, normally, φ is true” be said to follow from a given set of items of such information. Many answers to this question have been proposed but, surprisingly, virtually none have attempted any explicit connection to belief revision. The aim of this paper (...)
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  • Maxi-Adjustment and Possibilistic Deduction for Adaptive Information Agents.Raymond Lau, Arthur H. M. ter Hofstede & Peter D. Bruza - 2001 - Journal of Applied Non-Classical Logics 11 (1-2):169-201.
    The expressive power of logic is believed to be able to model most of the fundamental aspects of information retrieval. However, it is also understood that classical logic is ineffective for handling partiality and uncertainty in IR. Applying non-classical logics such as the AGM belief revision logic and the possibilistic logic to adaptive information retrieval is appealing since they provide a powerful and rigorous framework to model partiality and uncertainty inherent in any IR processes. The maxi-adjustment method, which is an (...)
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  • In conjunction with qualitative probability.Tim Fernando - 1998 - Annals of Pure and Applied Logic 92 (3):217-234.
    Numerical probabilities are eliminated in favor of qualitative notions, with an eye to isolating what it is about probabilities that is essential to judgements of acceptability. A basic choice point is whether the conjunction of two propositions, each acceptable, must be deemed acceptable. Concepts of acceptability closed under conjunction are analyzed within Keisler's weak logic for generalized quantifiers — or more specifically, filter quantifiers. In a different direction, the notion of a filter is generalized so as to allow sets with (...)
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  • Theorem proving for conditional logics: CondLean and GOALD U CK.Nicola Olivetti & Gian Luca Pozzato - 2008 - Journal of Applied Non-Classical Logics 18 (4):427-473.
    In this paper we focus on theorem proving for conditional logics. First, we give a detailed description of CondLean, a theorem prover for some standard conditional logics. CondLean is a SICStus Prolog implementation of some labeled sequent calculi for conditional logics recently introduced. It is inspired to the so called “lean” methodology, even if it does not fit this style in a rigorous manner. CondLean also comprises a graphical interface written in Java. Furthermore, we introduce a goal-directed proof search mechanism, (...)
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  • Roadmap for preferential logics.Dov M. Gabbay & Karl Schlechta - 2009 - Journal of Applied Non-Classical Logics 19 (1):43-95.
    We give a systematic overview of semantical and logical rules in non monotonic and related logics. We show connections and sometimes subtle differences, and also compare such rules to uses of the notion of size.
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  • To Preference via Entrenchment.Konstantinos Georgatos - 1999 - Annals of Pure and Applied Logic 96 (1--3):141--155.
    We introduce a simple generalization of Gardenfors and Makinson’s epistemic entrenchment called partial entrenchment. We show that preferential inference can be generated as the sceptical counterpart of an inference mechanism defined directly on partial entrenchment.
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