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David Makinson
London School of Economics
  1. On the Logic of Theory Change: Partial Meet Contraction and Revision Functions.Carlos E. Alchourrón, Peter Gärdenfors & David Makinson - 1985 - Journal of Symbolic Logic 50 (2):510-530.
    This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...)
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  2. The Paradox of the Preface.David C. Makinson - 1965 - Analysis 25 (6):205.
    By means of an example, shows the possibility of beliefs that are separately rational whilst together inconsistent.
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  3.  90
    On the Logic of Theory Change: Contraction Functions and Their Associated Revision Functions.Carlos E. Alchourron & David Makinson - 1982 - Theoria 48 (1):14-37.
    A study in the logic of theory change, examining the properties of maxichoice contraction and revision operations.
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  4. Bridges From Classical to Nonmonotonic Logic.David Makinson - 2005 - King's College Publications.
    An graduate level introduction to nonmonotonic reasoning, emphasizing structures and spirit common to different formulations, with exercises.
     
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  5. Input/Output Logics.David Makinson & Leendert van der Torre - 2000 - Journal of Philosophical Logic 29 (4):383-408.
    In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Examples arise in contexts of conditional obligations, goals, ideals, preferences, actions, and beliefs. Our purpose is to develop a theory of such input/output operations. Four are singled out: simple-minded, basic (making intelligent use of disjunctive inputs), simple-minded reusable (in which outputs may be recycled as inputs), and basic reusable. They (...)
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  6.  62
    On the Logic of Theory Change: Safe Contraction.Carlos E. Alchourrón & David Makinson - 1985 - Studia Logica 44 (4):405 - 422.
    This paper is concerned with formal aspects of the logic of theory change, and in particular with the process of shrinking or contracting a theory to eliminate a proposition. It continues work in the area by the authors and Peter Gärdenfors. The paper defines a notion of safe contraction of a set of propositions, shows that it satisfies the Gärdenfors postulates for contraction and thus can be represented as a partial meet contraction, and studies its properties both in general and (...)
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  7. 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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  8.  34
    On the Status of the Postulate of Recovery in the Logic of Theory Change.David Makinson - 1987 - Journal of Philosophical Logic 16 (4):383 - 394.
    Describes and discusses the rather special behaviour of one of the postulates in the AGM account of theory change.
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  9. General Patterns in Nonmonotonic Reasoning.David Makinson - 1994 - In Handbook of Logic in Artificial Intelligence Nad Logic Programming, Vol. Iii. Oxford: Clarendon Press. pp. 35-110.
    An extended review of what is known about the formal behaviour of nonmonotonic inference operations, including those generated by the principal systems in the artificial intelligence literature. Directed towards computer scientists and others with some background in logic.
     
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  10.  71
    Conditional Probability in the Light of Qualitative Belief Change.David C. Makinson - 2011 - Journal of Philosophical Logic 40 (2):121 - 153.
    We explore ways in which purely qualitative belief change in the AGM tradition throws light on options in the treatment of conditional probability. First, by helping see why it can be useful to go beyond the ratio rule defining conditional from one-place probability. Second, by clarifying what is at stake in different ways of doing that. Third, by suggesting novel forms of conditional probability corresponding to familiar variants of qualitative belief change, and conversely. Likewise, we explain how recent work on (...)
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  11.  56
    Constraints for Input/Output Logics.David Makinson & Leendert van der Torre - 2001 - Journal of Philosophical Logic 30 (2):155 - 185.
    In a previous paper we developed a general theory of input/output logics. These are operations resembling inference, but where inputs need not be included among outputs, and outputs need not be reusable as inputs. In the present paper we study what happens when they are constrained to render output consistent with input. This is of interest for deontic logic, where it provides a manner of handling contrary-to-duty obligations. Our procedure is to constrain the set of generators of the input/output system, (...)
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  12.  49
    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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  13.  34
    Hierarchies of Regulations and Their Logic.Carlos E. Alchourrón & David Makinson - 1981 - In Risto Hilpinen (ed.), New Studies in Deontic Logic. Dordrecht: Reidel. pp. 125--148.
    Investigates the resolution of contradictions and ambiguous derogations in a code, by means of the imposition of partial orderings.
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  14.  54
    How to Give It Up: A Survey of Some Formal Aspects of the Logic of Theory Change.David Makinson - 1985 - Synthese 62 (3):347 - 363.
    The paper surveys some recent work on formal aspects of the logic of theory change. It begins with a general discussion of the intuitive processes of contraction and revision of a theory, and of differing strategies for their formal study. Specific work is then described, notably Gärdenfors'' postulates for contraction and revision, maxichoice contraction and revision functions and the condition of orderliness, partial meet contraction and revision functions and the condition of relationality, and finally the operations of safe contraction and (...)
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  15.  11
    Input/Output Logics.David Makinson & Leendert Van Der Torre - 2000 - Journal of Philosophical Logic 29 (4):383 - 408.
    In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Examples arise in contexts of conditional obligations, goals, ideals, preferences, actions, and beliefs. Our purpose is to develop a theory of such input/output operations. Four are singled out: simple-minded, basic (making intelligent use of disjunctive inputs), simple-minded reusable (in which outputs may be recycled as inputs), and basic reusable. They (...)
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  16.  24
    Some Embedding Theorems for Modal Logic.David Makinson - 1971 - Notre Dame Journal of Formal Logic 12 (2):252-254.
    Some results on the upper end of the lattice of all modal propositional logics.
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  17.  77
    The Logic of Inconsistency: A Study in Nonstandard Possible-World Semantics and Ontology.David Makinson - 1979 - American Philosophical Quarterly, Library of Philosophy 5 (1):233-236.
  18.  20
    Relations Between the Logic of Theory Change and Nonmonotonic Logic.David Makinson & Peter Gärdenfors - 1991 - In André Fuhrmann & Michael Morreau (eds.), The Logic of Theory Change. Springer. pp. 183--205.
    Examines the link between nonmonotonic inference relations and theory revision operations, focusing on the correspondence between abstract properties which each may satisfy.
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  19.  36
    Screened Revision.David Makinson - 1997 - Theoria 63 (1-2):14-23.
    Develops a concept of revision, akin in spirit to AGM partial meet revision, but in which the postulate of 'success' may fail. The basic idea is to see such an operation as composite, with a pre-processor using a priori considerations to resolve the question of whether to revise, following which another operation revises in a manner that protects the a priori material.
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  20.  49
    Permission From an Input/Output Perspective.David Makinson & Leendert van der Torre - 2003 - Journal of Philosophical Logic 32 (4):391 - 416.
    Input/output logics are abstract structures designed to represent conditional obligations and goals. In this paper we use them to study conditional permission. This perspective provides a clear separation of the familiar notion of negative permission from the more elusive one of positive permission. Moreover, it reveals that there are at least two kinds of positive permission. Although indistinguishable in the unconditional case, they are quite different in conditional contexts. One of them, which we call static positive permission, guides the citizen (...)
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  21. A Normal Modal Calculus Between T and S4 Without the Finite Model Property.David Makinson - 1969 - Journal of Symbolic Logic 34 (1):35-38.
    The first example of an intuitively meaningful propositional logic without the finite model property, and still the simplest one in the literature. The question of its decidability appears still to be open.
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  22.  10
    Deontic Logic.David Makinson & Lennart Aqvist - 1989 - Journal of Symbolic Logic 54 (4):1481.
  23.  26
    Counterfactuals.David Makinson - 1974 - Studia Logica 33 (4):425-427.
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  24.  1
    Nonmonotonic Inference Based on Expectations.Peter Gärdenfors & David Makinson - 1994 - Artificial Intelligence 65 (2):197-245.
  25.  39
    On the Formal Representation of Rights Relations.David Makinson - 1986 - Journal of Philosophical Logic 15 (4):403 - 425.
    A discussion of work formalising Hohfeld's classic taxonomy of rights relations between two parties.
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  26.  12
    Bridges Between Classical and Nonmonotonic Logic.David Makinson - 2003 - Logic Journal of the IGPL 11 (1):69-96.
    The purpose of this paper is to take some of the mystery out of what is known as nonmonotonic logic, by showing that it is not as unfamiliar as may at first sight appear. In fact, it is easily accessible to anybody with a background in classical propositional logic, provided that certain misunderstandings are avoided and a tenacious habit is put aside. In effect, there are logics that act as natural bridges between classical consequence and the principal kinds of nonmonotonic (...)
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  27.  64
    Maps Between Some Different Kinds of Contraction Function: The Finite Case.Carlos E. Alchourrón & David Makinson - 1986 - Studia Logica 45 (2):187 - 198.
    In some recent papers, the authors and Peter Gärdenfors have defined and studied two different kinds of formal operation, conceived as possible representations of the intuitive process of contracting a theory to eliminate a proposition. These are partial meet contraction (including as limiting cases full meet contraction and maxichoice contraction) and safe contraction. It is known, via the representation theorem for the former, that every safe contraction operation over a theory is a partial meet contraction over that theory. The purpose (...)
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  28.  50
    How to Give It Up: A Survey of Some Formal Aspects of the Logic of Theory Change.David Makinson - 1986 - Synthese 68 (1):185 - 186.
    The paper surveys some recent work on formal aspects of the logic of theory change. It begins with a general discussion of the intuitive processes of contraction and revision of a theory, and of differing strategies for their formal study. Specific work is then described, notably Gärdenfors' postulates for contraction and revision, maxichoice contraction and revision functions and the condition of orderliness, partial meet contraction and revision functions and the condition of relationality, and finally the operations of safe contraction and (...)
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  29.  42
    Parallel Interpolation, Splitting, and Relevance in Belief Change.George Kourousias & David C. Makinson - 2007 - Journal of Symbolic Logic 72 (3):994-1002.
    The splitting theorem says that any set of formulae has a finest representation as a family of letter-disjoint sets. Parikh formulated this for classical propositional logic, proved it in the finite case, used it to formulate a criterion for relevance in belief change, and showed that AGMpartial meet revision can fail the criterion. In this paper we make three further contributions. We begin by establishing a new version of the well-known interpolation theorem, which we call parallel interpolation, use it to (...)
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  30.  16
    Propositional Relevance Through Letter-Sharing.David Makinson - 2009 - Journal of Applied Logic 7 (4):377-387.
    The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a long time. But it began to take on a fresh life in the late 1990s when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh: the relation of relevance was considered modulo the choice of a background belief set, and the belief set was put into a (...)
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  31.  37
    A Warning About the Choice of Primitive Operators in Modal Logic.David Makinson - 1973 - Journal of Philosophical Logic 2 (2):193 - 196.
    Draws attention to some unexpected consequences of using a zero-ary connective in modal propositional logic.
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  32.  38
    How Meaningful Are Modal Operators?David Makinson - 1966 - Australasian Journal of Philosophy 44 (3):331 – 337.
    A philosophical discussion of the intuitive meaning of the formalism of modal propositional logics.
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  33.  16
    The Logic of Inconsistency. A Study in Non-Standard Possible-World Semantics and Ontology.David Makinson - 1979 - Journal of Symbolic Logic 47 (1):233-236.
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  34.  29
    A Generalisation of the Concept of a Relational Model for Modal Logic.David Makinson - 1970 - Theoria 36 (3):331-335.
    Generalises the concept of a relational model for modal logic, due to Kripke, so as to obtain a closer correspondence between relational and algebraic models. The generalisation obtained is essentially equivalent to the notion of a "first-order" model that was defined independently by S.K.Thomason.
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  35.  33
    The Gärdenfors Impossibility Theorem in Non-Monotonic Contexts.David Makinson - 1990 - Studia Logica 49 (1):1 - 6.
    Gärdenfors' impossibility theorem draws attention to certain formal difficulties in defining a conditional connective from a notion of theory revision, via the Ramsey test. We show that these difficulties are not avoided by taking the background inference operation to be non-monotonic.
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  36.  1
    Doing the Best We Can. An Essay in Informal Deontic Logic.David Makinson - 1987 - Journal of Symbolic Logic 52 (4):1050-1051.
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  37.  32
    On an Inferential Semantics for Classical Logic.David C. Makinson - 2014 - Logic Journal of the IGPL 22 (1):147-154.
    We seek a better understanding of why an inferential semantics devised by Tor Sandqvist yields full classical logic, by providing and analysing a direct proof via a suitable maximality construction.
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  38.  43
    Post Completeness and Ultrafilters.David Makinson & Krister Segerberg - 1974 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 20 (25-27):385-388.
    A cardinality result in modal propositional logic.
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  39.  15
    Relevance Via Decomposition.David Makinson - 2017 - Australasian Journal of Logic 14 (3).
    We report on progress and an unsolved problem in our attempt to obtain a clear rationale for relevance logic via semantic decomposition trees. Suitable decomposition rules, constrained by a natural parity condition, generate a set of directly acceptable formulae that contains all axioms of the well-known system R, is closed under substitution and conjunction, satisfies the letter-sharing condition, but is not closed under detachment. To extend it, a natural recursion is built into the procedure for constructing decomposition trees. The resulting (...)
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  40.  61
    Respecting Relevance in Belief Change.David C. Makinson & George Kourousias - 2006 - Análisis Filosófico 26 (1):53-61.
    In this paper dedicated to Carlos Alchourrón, we review an issue that emerged only after his death in 1996, but would have been of great interest to him: To what extent do the formal operations of AGM belief change respect criteria of relevance? A natural criterion was proposed in 1999 by Rohit Parikh, who observed that the AGM model does not always respect it. We discuss the pros and cons of this criterion, and explain how the AGM account may be (...)
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  41.  27
    Remarks on the Concept of Distribution in Traditional Logic.David Makinson - 1969 - Noûs 3 (1):103-108.
    Uses ideas of mathematical logic to clarify and to a certain extent defend a controverted and rather obscure notion of traditional syllogistic.
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  42.  38
    Stenius' Approach to Disjunctive Permission.David Makinson - 1984 - Theoria 50 (2-3):138-147.
    A critical review of Stenius' account of the logic of disjunctive permissions, leading to a proposal for a closely related approach in terms of "checklist conditionals".
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  43.  11
    Intelim Rules for Classical Connectives.David C. Makinson - 2014 - In .
    We investigate introduction and elimination rules for truth-functional connectives, focusing on the general questions of the existence, for a given connective, of at least one such rule that it satisfies, and the uniqueness of a connective with respect to the set of all of them. The answers are straightforward in the context of rules using general set/set sequents of formulae, but rather complex and asymmetric in the restricted context of set/formula sequents, as also in the intermediate set/formula-or-empty context.
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  44.  38
    Propositional Relevance Through Letter-Sharing: Review and Contribution.David C. Makinson - unknown
    The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a very long time. But it began to take on a fresh life in 1999 when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh. First, the relation of relevance was considered modulo the belief set under consideration, Second, the belief set was put in a canonical form, (...)
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  45.  16
    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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  46.  24
    Friendliness and Sympathy in Logic.David C. Makinson - 2005 - In Jean-Yves Beziau (ed.), Logica Universalis. Birkhäuser Verlog. pp. 191-206.
    We define and examine a notion of logical friendliness, which is a broadening of the familiar notion of classical consequence. The concept is tudied first in its simplest form, and then in a syntax-independent version, which we call sympathy. We also draw attention to the surprising number of familiar notions and operations with which it makes contact, providing a new light in which they may be seen.
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  47.  24
    Friendliness for Logicians.David C. Makinson - 2005 - In Sergei Artemov, H. Barringer, A. S. D'Avila Garcez, L. C. Lamb & J. Woods (eds.), We Will Show Them! Essays in Honour of Dov Gabbay. London: College Publications. pp. 259-292.
    We define and examine a notion of logical friendliness, which is a broadening of the familiar notion of classical consequence. The concept is studied first in its simplest form, and then in a syntax-independent version, which we call sympathy. We also draw attention to the surprising number of familiar notions and operations with which it makes contact, providing a new light in which they may be seen.
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  48. Logical Questions Behind the Lottery and Preface Paradoxes: Lossy Rules for Uncertain Inference.David Makinson - 2012 - Synthese 186 (2):511-529.
    We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied in its absence, and a partial rehabilitation of conjunction as a ‘lossy’ rule. A second lesson is the (...)
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  49. In memoriam carlos eduardo alchourron.David Makinson - 1996 - Nordic Journal of Philosophical Logic 1 (1):3-10.
    Obituary notice with overview of the work of Carlos Alchourrón, focussing on his contributions to the logic of theory change.
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  50.  88
    Intuitionistic Logic and Elementary Rules.Lloyd Humberstone & David Makinson - 2011 - Mind 120 (480):1035-1051.
    The interplay of introduction and elimination rules for propositional connectives is often seen as suggesting a distinguished role for intuitionistic logic. We prove three formal results concerning intuitionistic propositional logic that bear on that perspective, and discuss their significance. First, for a range of connectives including both negation and the falsum, there are no classically or intuitionistically correct introduction rules. Second, irrespective of the choice of negation or the falsum as a primitive connective, classical and intuitionistic consequence satisfy exactly the (...)
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