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  1. David C. Makinson, Intelim Rules for Classical Connectives.
    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 (but more often used) context of set/formula sequents, as also in the intermediate (...)
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  2. David C. Makinson, On an Inferential Semantics for Classical Logic.
    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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  3. David C. Makinson, Relevance Logic as a Conservative Extension of Classical Logic.
    Relevance logic is ordinarily seen as a subsystem of classical logic under the translation that replaces arrows by horseshoes. If, however, we consider the arrow as an additional connective alongside the horseshoe, then another perspective emerges: the theses of relevance logic, specifically the system R, may also be seen as the output of a conservative extension of the relation of classical consequence. We describe two ways in which this may be done. One is by defining a suitable closure relation out (...)
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  4. David Makinson (2012). Dov M. Gabbay and Karl Schlechta , Conditionals and Modularity in General Logics . Reviewed By. Philosophy in Review 32 (5):376-378.
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  5. David Makinson (2012). Logical Questions Behind the Lottery and Preface Paradoxes: Lossy Rules for Uncertain Inference. 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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  6. Karl Schlechta & David Makinson (2012). Local and Global Metrics for the Semantics of Counterfactual Conditionals. Journal of Applied Non-Classical Logics 4 (2):129-140.
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  7. David Makinson (2011). Conditional Probability in the Light of Qualitative Belief Change. 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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  8. David Makinson (2009). Levels of Belief in Nonmonotonic Reasoning. In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Springer. 341--354.
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  9. David C. Makinson, Propositional Relevance Through Letter-Sharing.
    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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  10. James Hawthorne & David Makinson (2007). The Quantitative/Qualitative Watershed for Rules of Uncertain Inference. 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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  11. George Kourousias & David C. Makinson (2007). Parallel Interpolation, Splitting, and Relevance in Belief Change. 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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  12. David C. Makinson, Completeness Theorems, Representation Theorems: What's the Difference?
    Most areas of logic can be approached either semantically or syntactically. Typically, the approaches are linked through a completeness or representation theorem. The two kinds of theorem serve a similar purpose, yet there also seems to be some residual distinction between them. In what respects do they differ, and how important are the differences? Can we have one without the other? We discuss these questions, with examples from a variety of different logical systems.
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  13. David Makinson & George Kourousias (2006). Respecting Relevance in Belief Change. 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 (but also debateable) 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 (...)
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  14. David Makinson (2005). Bridges From Classical to Nonmonotonic Logic. King's College Publications.
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  15. David C. Makinson (2005). Friendliness and Sympathy in Logic. In J. Y. Beziau (ed.), Logica Universalis. Birkhäuser Verlog. 191--206.
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  16. David C. Makinson, Friendliness for Logicians.
    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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  17. David C. Makinson (2005). Logical Friendliness and Sympathy in Logic. In J. Y. Beziau (ed.), Logica Universalis. Birkhäuser Verlog. 191--205.
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  18. David Makinson & Leendert van der Torre (2003). Permission From an Input/Output Perspective. 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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  19. David Makinson & Leendert van der Torre (2003). Permission From an Input/Output Perspective. 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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  20. David Makinson & Leendert van der Torre (2001). Constraints for Input/Output Logics. 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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  21. David Makinson & Leendert van der Torre (2001). Constraints for Input/Output Logics. 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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  22. David Makinson & Leendert Van Der Torre (2000). Input/Output Logics. 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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  23. David Makinson & Leendert van der Torre (2000). Input/Output Logics. 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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  24. David Makinson (1996). Combinatorial Versus Decision-Theoretic Components of Impossibility Theorems. Theory and Decision 40 (2):181-189.
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  25. David Makinson (1996). In memoriam carlos eduardo alchourron. Nordic Journal of Philosophical Logic 1 (1):3-10.
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  26. David Makinson (1994). General Patterns in Nonmonotonic Reasoning. In Handbook of Logic in Artificial Intelligence Nad Logic Programming, Vol. Iii. Clarendon Press.
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  27. David Makinson (1994). Handbook of Logic in Artificial Intelligence Nad Logic Programming, Vol. Iii. Clarendon Press.
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  28. David Makinson (1993). Five Faces of Minimality. 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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  29. Jürgen Dix & David Makinson (1992). The Relationship Between KLM and MAK Models for Nonmonotonic Inference Operations. Journal of Logic, Language and Information 1 (2):131-140.
    The purpose of this note is to make quite clear the relationship between two variants of the general notion of a preferential model for nonmonotonic inference: the models of Kraus, Lehmann and Magidor (KLM models) and those of Makinson (MAK models).On the one hand, we introduce the notion of the core of a KLM model, which suffices to fully determine the associated nonmonotonic inference relation. On the other hand, we slightly amplify MAK models with a monotonic consequence operation as additional (...)
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  30. David Makinson & Peter Gärdenfors (1991). Relations Between the Logic of Theory Change and Nonmonotonic Logic. In André Fuhrmann & Michael Morreau (eds.), The Logic of Theory Change. Springer. 183--205.
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  31. David Makinson (1990). The Gärdenfors Impossibility Theorem in Non-Monotonic Contexts. 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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  32. David Makinson (1989). On Attributing Rights to All Peoples: Some Logical Questions. [REVIEW] Law and Philosophy 8 (1):53 - 63.
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  33. David Makinson (1989). Review: Lennart Aqvist, Deontic Logic. [REVIEW] Journal of Symbolic Logic 54 (4):1481-1483.
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  34. David Makinson (1987). On the Status of the Postulate of Recovery in the Logic of Theory Change. Journal of Philosophical Logic 16 (4):383 - 394.
  35. David Makinson (1987). Review: Fred Feldman, Doing the Best We Can. An Essay in Informal Deontic Logic. [REVIEW] Journal of Symbolic Logic 52 (4):1050-1051.
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  36. Carlos E. Alchourrón & David Makinson (1986). Maps Between Some Different Kinds of Contraction Function: The Finite Case. 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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  37. David Makinson (1986). How to Give It Up: A Survey of Some Formal Aspects of the Logic of Theory Change. 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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  38. David Makinson (1986). On the Formal Representation of Rights Relations. Journal of Philosophical Logic 15 (4):403 - 425.
  39. Carlos E. Alchourrón, Peter Gärdenfors & David Makinson (1985). On the Logic of Theory Change: Partial Meet Contraction and Revision Functions. 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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  40. Carlos E. Alchourrón & David Makinson (1985). On the Logic of Theory Change: Safe Contraction. 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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  41. David Makinson (1985). How to Give It Up: A Survey of Some Formal Aspects of the Logic of Theory Change. 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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  42. David Makinson (1984). Stenius' Approach to Disjunctive Permission. Theoria 50 (2-3):138-147.
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  43. Carlos E. Alchourron & David Makinson (1982). On the Logic of Theory Change: Contraction Functions and Their Associated Revision Functions. Theoria 48 (1):14-37.
  44. David Makinson (1982). Review: Nicholas Rescher, Robert Brandom, The Logic of Inconsistency. A Study in Non-Standard Possible-World Semantics and Ontology. [REVIEW] Journal of Symbolic Logic 47 (1):233-236.
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  45. Carlos E. Alchourrón & David Makinson (1981). Hierarchies of Regulations and Their Logic. In Risto Hilpinen (ed.), New Studies in Deontic Logic. 125--148.
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  46. David Makinson (1981). Non‐Equivalent Formulae in One Variable in A Strong Omnitemporal Modal Logic. Mathematical Logic Quarterly 27 (7):111-112.
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  47. David Makinson (1981). Quantificational Reefs in Deontic Waters. In Risto Hilpinen (ed.), New Studies in Deontic Logic. 87--91.
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  48. David Makinson (1981). Review: Brian F. Chellas, Modal Logic. An Introduction. [REVIEW] Journal of Symbolic Logic 46 (3):670-672.
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  49. David Makinson (1975). Review: Arthur Pap, Logic and the Concept of Entailment. [REVIEW] Journal of Symbolic Logic 40 (3):466-466.
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  50. David Makinson (1975). Review: Alan Rose, Extensions of Some Theorems of Anderson and Belnap. [REVIEW] Journal of Symbolic Logic 40 (3):466-466.
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