Results for 'relational logic'

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  1. Relating Logics of Justification and Evidence.Igor Sedlár - 2014 - In Vít Punčochář & Michal Dančák (eds.), The Logica Yearbook 2013. College Publications. pp. 207-222.
    The paper relates evidence and justification logics, both philosophically and technically. On the philosophical side, it is suggested that the difference between the approaches to evidence in the two families of logics can be explained as a result of their focusing on two different notions of support provided by evidence. On the technical side, a justification logic with operators pertaining to both kinds of support is shown to be sound and complete with respect to a special class of awareness (...)
     
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  2.  35
    Dynamic Relation Logic is the Logic of DPL-Relations.Albert Visser - 1997 - Journal of Logic, Language and Information 6 (4):441-452.
    In this paper we prove that the principles in the languagewith relation composition and dynamic implication, valid forall binary relations, are the same ones as the principlesvalid when we restrict ourselves to DPL-relations,i.e. relations generated from conditions (tests) and resettings.
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  3.  20
    Relational Logics and Their Applications.Joanna Golińska-Pilarek & Ewa Orłowska - 2006 - In Harrie de Swart, Ewa Orlowska, Gunther Smith & Marc Roubens (eds.), Theory and Applications of Relational Structures as Knowledge Instruments Ii. Springer. pp. 125.
    Logics of binary relations corresponding, among others, to the class RRA of representable relation algebras and the class FRA of full relation algebras are presented together with the proof systems in the style of dual tableaux. Next, the logics are extended with relational constants interpreted as point relations. Applications of these logics to reasoning in non-classical logics are recalled. An example is given of a dual tableau proof of an equation which is RRA-valid, while not RA-valid.
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  4.  8
    Distributed Relation Logic.Gerard Allwein, William L. Harrison & Thomas Reynolds - 2017 - Logic and Logical Philosophy 26 (1):19-61.
    We extend the relational algebra of Chin and Tarski so that it is multisorted or, as we prefer, typed. Each type supports a local Boolean algebra outfitted with a converse operator. From Lyndon, we know that relation algebras cannot be represented as proper relation algebras where a proper relation algebra has binary relations as elements and the algebra is singly-typed. Here, the intensional conjunction, which was to represent relational composition in Chin and Tarski, spans three different local algebras, (...)
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  5.  15
    The Relational Logic of Franciscus Toletus and Petrus Fonseca.Petr Dvořák - 2009 - Forum Philosophicum: International Journal for Philosophy 14 (1):87-99.
    The well-known Ratio Studiorum of 1599 states that logical instruction should follow F. Toletus or P. Fonseca. The latter authored the famous Institutionum Dialecticarum Libri Octo , the former a similar manual, Introductio in Dialecticam Aristotelis . As is often observed, the contrast between the Aristotelian and present symbolic logics is perhaps most striking in their analysis of relational statements. Both authors recognize the relational logical form as independent from the traditional subject-predicate form and see the need to (...)
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  6.  1
    The Relational Logic of Franciscus Toletus and Petrus Fonseca.Petr Dvořák - 2009 - Forum Philosophicum: International Journal for Philosophy 14 (1):87-99.
    The well-known Ratio Studiorum of 1599 states that logical instruction should follow F. Toletus or P. Fonseca. The latter authored the famous Institutionum Dialecticarum Libri Octo, the former a similar manual, Introductio in Dialecticam Aristotelis. As is often observed, the contrast between the Aristotelian and present symbolic logics is perhaps most striking in their analysis of relational statements. Both authors recognize the relational logical form as independent from the traditional subject-predicate form and see the need to recognize (...) inferential rules. They differ in their specific rules, however, so neither of the authors has captured the system of relational syllogism in its entirety. (shrink)
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  7. Relational Logics for Formalization of Database Dependencies.Wojciech Buszkowski & Ewa Orlowska - 1998 - Bulletin of the Section of Logic 27.
     
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  8.  10
    Dual Tableau-Based Decision Procedures for Relational Logics with Restricted Composition Operator.Domenico Cantone, Marianna Nicolosi Asmundo & Ewa Orlowska - 2011 - Journal of Applied Non-Classical Logics 21 (2):177-200.
    We consider fragments of the relational logic RL obtained by posing various constraints on the relational terms involving the operator of composition of relations. These fragments allow to express several non classical logics including modal and description logics. We show how relational dual tableaux can be employed to provide decision procedures for each of them.
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  9. Plato's Epistemology and Related Logical Problems. Plato - 1972 - London: Faber.
  10.  14
    Classical and Relational Logic.Roger W. Holmes - 1936 - Philosophical Review 45 (3):297-303.
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  11. Logically Simple Properties and Relations.Jan Plate - 2016 - Philosophers' Imprint 16:1-40.
    This paper presents an account of what it is for a property or relation (or ‘attribute’ for short) to be logically simple. Based on this account, it is shown, among other things, that the logically simple attributes are in at least one important way sparse. This in turn lends support to the view that the concept of a logically simple attribute can be regarded as a promising substitute for Lewis’s concept of a perfectly natural attribute. At least in part, the (...)
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  12.  31
    On the Computational Complexity of the Numerically Definite Syllogistic and Related Logics.Ian Pratt-Hartmann - 2008 - Bulletin of Symbolic Logic 14 (1):1-28.
    The numerically definite syllogistic is the fragment of English obtained by extending the language of the classical syllogism with numerical quantifiers. The numerically definite relational syllogistic is the fragment of English obtained by extending the numerically definite syllogistic with predicates involving transitive verbs. This paper investigates the computational complexity of the satisfiability problem for these fragments. We show that the satisfiability problem (= finite satisfiability problem) for the numerically definite syllogistic is strongly NP-complete, and that the satisfiability problem (= (...)
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  13. Logical Relations Between Pictures.Jan Westerhoff - 2005 - Journal of Philosophy 102 (12):603 - 623.
    An implication relation between pictures is defined, it is then shown how conjunctions, disjunctions, negations, and hypotheticals of pictures can be formed on the basis of this. It is argued that these logical operations on pictures correspond to natural cognitive operations employed when thinking about pictures.
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  14.  13
    Relational Approach for a Logic for Order of Magnitude Qualitative Reasoning with Negligibility, Non-Closeness and Distance.Joanna Golinska-Pilarek & Emilio Munoz Velasco - 2009 - Logic Journal of the IGPL 17 (4):375–394.
    We present a relational proof system in the style of dual tableaux for a multimodal propositional logic for order of magnitude qualitative reasoning to deal with relations of negligibility, non-closeness, and distance. This logic enables us to introduce the operation of qualitative sum for some classes of numbers. A relational formalization of the modal logic in question is introduced in this paper, i.e., we show how to construct a relational logic associated with the (...)
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  15. Logical Expressivism and Logical Relations.Lionel Shapiro - 2018 - In Ondřej Beran, Vojtěch Kolman & Ladislav Koreň (eds.), From rules to meanings. New essays on inferentialism. New York: Routledge. pp. 179-95.
    According to traditional logical expressivism, logical operators allow speakers to explicitly endorse claims that are already implicitly endorsed in their discursive practice — endorsed in virtue of that practice’s having instituted certain logical relations. Here, I propose a different version of logical expressivism, according to which the expressive role of logical operators is explained without invoking logical relations at all, but instead in terms of the expression of discursive-practical attitudes. In defense of this alternative, I present a deflationary account of (...)
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  16.  65
    Jack H. Silver. Counting the Number of Equivalence Classes of Borel and Coanalytic Equivalence Relations. Annals of Mathematical Logic, Vol. 18 , Pp. 1–28. - John P. Burgess. Equivalences Generated by Families of Borel Sets. Proceedings of the American Mathematical Society. Vol. 69 , Pp. 323–326. - John P. Burgess. A Reflection Phenomenon in Descriptive Set Theory. Fundamenta Mathematicae. Vol. 104 , Pp. 127–139. - L. Harrington and R. Sami. Equivalence Relations, Projective and Beyond. Logic Colloquium '78, Proceedings of the Colloquium Held in Mons, August 1978, Edited by Maurice Boffa, Dirk van Dalen, and Kenneth McAloon, Studies in Logic and the Foundations of Mathematics, Vol. 97, North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1979, Pp. 247–264. - Leo Harrington and Saharon Shelah. Counting Equivalence Classes for Co-Κ-Souslin Equivalence Relations. Logic Colloquium '80, Papers Intended for the European Summer Meeting of the Association for Symbolic Logic, Edit. [REVIEW]Alain Louveau - 1987 - Journal of Symbolic Logic 52 (3):869-870.
  17.  2
    Formal Methods for Nonmonotonic and Related Logics: Vol I: Preference and Size.Karl Schlechta - 2018 - Springer Verlag.
    The two volumes in this advanced textbook present results, proof methods, and translations of motivational and philosophical considerations to formal constructions. In this Vol. I the author explains preferential structures and abstract size. In the associated Vol. II he presents chapters on theory revision and sums, defeasible inheritance theory, interpolation, neighbourhood semantics and deontic logic, abstract independence, and various aspects of nonmonotonic and other logics. In both volumes the text contains many exercises and some solutions, and the author limits (...)
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  18.  2
    Formal Methods for Nonmonotonic and Related Logics: Vol Ii: Theory Revision, Inheritance, and Various Abstract Properties.Karl Schlechta - 2018 - Springer Verlag.
    The two volumes in this advanced textbook present results, proof methods, and translations of motivational and philosophical considerations to formal constructions. In the associated Vol. I the author explains preferential structures and abstract size. In this Vol. II he presents chapters on theory revision and sums, defeasible inheritance theory, interpolation, neighbourhood semantics and deontic logic, abstract independence, and various aspects of nonmonotonic and other logics. In both volumes the text contains many exercises and some solutions, and the author limits (...)
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  19. Logics for the Relational Syllogistic.Ian Pratt-Hartmann & Lawrence S. Moss - 2009 - Review of Symbolic Logic 2 (4):647-683.
    The Aristotelian syllogistic cannot account for the validity of certain inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subject noun phrase may contain a relative clause. The logics we present are extensions of the classical syllogistic, and we pay special attention to the question of (...)
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  20.  18
    Stevo Todorčević, Forcing Positive Partition Relations, Transactions of the American Mathematical Society, Vol. 280 , Pp. 703–720. - Stevo Todorčević, Directed Sets and Cofinal Types, Transactions of the American Mathematical Society, Vol. 290 , Pp. 711–723. - Stevo Todorčević, Reals and Positive Partition Relations, Logic, Methodology and Philosophy of Science VII, Proceedings of the Seventh International Congress of Logic, Methodology and Philosophy of Science, Salzburg, 1983, Edited by Ruth Barcan Marcus, Georg J. W. Dorn, and Paul Weingartner, Studies in Logic and the Foundations of Mathematics, Vol. 114, North-Holland, Amsterdam, New York, Oxford, and Tokyo, 1986, Pp. 159–169. - Stevo Todorčević, Remarks on Chain Conditions in Products, Compositio Mathematica, Vol. 55 , Pp. 295–302. - Stevo Todorčević, Remarks on Cellularity in Products, Compositio Mathematica, Vol. 57 , Pp. 357–372. - Stevo Todorčević, Partition Relations for Partially Ordered Sets, Acta Mathematica, Vol. 155 , P. [REVIEW]Alan Dow - 1989 - Journal of Symbolic Logic 54 (2):635-638.
  21.  13
    Keene G. B.. The Relational Syllogism. A Systematic Approach to Relational Logic. University of Exeter, Exeter 1969, Iv + 35 Pp. [REVIEW]Gerald J. Massey - 1970 - Journal of Symbolic Logic 35 (3):448-450.
  22. Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method.Carlo Cellucci - 2013 - Dordrecht, Netherland: Springer.
    This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it (...)
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  23.  28
    The Relations Between Logic and Philosophy, 1874-1931.Leila Haaparanta - 2008 - In The Development of Modern Logic. Oxford University Press. pp. 222.
    This chapter gives a survey of the field of philosophy where the philosophical foundations of modern logic were discussed and where such themes of logic were discussed that were on the borderline between logic and other branches of the philosophical enterprise, such as metaphysics and epistemology. The contributions made by Gottlob Frege and Charles Peirce are included since their work in logic is closely related to and also strongly motivated by their philosophical views and interests. In (...)
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  24.  78
    Relevance Logic and the Calculus of Relations.Roger D. Maddux - 2010 - Review of Symbolic Logic 3 (1):41-70.
    Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.
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  25.  12
    The Relational Syllogism: A Systematic Approach to Relational Logic.Geoffrey Bourton Keene - 1962 - Exeter, England: Exeter, University of Exeter.
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  26.  22
    Plato's Epistemology Gwynneth Matthews: Plato's Epistemology and Related Logical Problems. Pp. 267. London: Faber, 1972. Stiff Paper, £1·95. [REVIEW]D. W. Hamlym - 1975 - The Classical Review 25 (01):18-20.
  27.  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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  28.  49
    Modal Logics with Linear Alternative Relations.Krister Segerberg - 1970 - Theoria 36 (3):301-322.
  29.  63
    The Relation Between Ontology and Logic in Kant.Clinton Tolley - 2016 - Internationales Jahrbuch des Deutschen Idealismus 12:75-98.
  30.  6
    Review: G. B. Keene, The Relational Syllogism. A Systematic Approach to Relational Logic[REVIEW]Gerald J. Massey - 1970 - Journal of Symbolic Logic 35 (3):448-450.
  31.  71
    Propositional Logics Related to Heyting's and Johansson's.Krister Segerberg - 1968 - Theoria 34 (1):26-61.
  32.  25
    Relational Semantics of the Lambek Calculus Extended with Classical Propositional Logic.Michael Kaminski & Nissim Francez - 2014 - Studia Logica 102 (3):479-497.
    We show that the relational semantics of the Lambek calculus, both nonassociative and associative, is also sound and complete for its extension with classical propositional logic. Then, using filtrations, we obtain the finite model property for the nonassociative Lambek calculus extended with classical propositional logic.
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  33.  95
    Relations Vs Functions at the Foundations of Logic: Type-Theoretic Considerations.Paul Oppenheimer & Edward N. Zalta - 2011 - Journal of Logic and Computation 21:351-374.
    Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in terms of relations (using the definite description operator). We argue that there is a reason to prefer Whitehead & Russell's reduction of functions to relations over Frege's reduction of relations to functions. There (...)
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  34.  4
    The Relational Syllogism. A Systematic Approach to Relational Logic.Gerald J. Massey - 1970 - Journal of Symbolic Logic 35 (3):448-450.
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  35. Relational Syllogisms and the History of Arabic Logic, 900-1900.Khaled El-Rouayheb - 2010 - Brill.
    Relational inferences are a well-known problem for Aristotelian logic. This book charts the development of thinking about this problem by logicians writing in Arabic from the ninth to the nineteenth century. It shows that that the development of Arabic logic did not - as is often supposed - come to an end in the fourteenth century.
     
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  36.  10
    Review: Roger W. Holmes, Classical and Relational Logic[REVIEW]Charles A. Baylis - 1936 - Journal of Symbolic Logic 1 (2):69-69.
  37.  51
    Modal Logics for Reasoning About Infinite Unions and Intersections of Binary Relations.Natasha Alechina, Philippe Balbiani & Dmitry Shkatov - 2012 - Journal of Applied Non-Classical Logics 22 (4):275 - 294.
    (2012). Modal logics for reasoning about infinite unions and intersections of binary relations. Journal of Applied Non-Classical Logics: Vol. 22, No. 4, pp. 275-294. doi: 10.1080/11663081.2012.705960.
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  38. Logical Normativity and Rational Agency—Reassessing Locke's Relation to Logic.Huaping Lu-Adler - 2018 - Journal of the History of Philosophy 56 (1):75-99.
    There is an exegetical quandary when it comes to interpreting Locke's relation to logic.On the one hand, over the last few decades a substantive amount of literature has been dedicated to explaining Locke's crucial role in the development of a new logic in the seventeenth and eighteenth centuries. John Yolton names this new logic the "logic of ideas," while James Buickerood calls it "facultative logic."1 Either way, Locke's Essay is supposedly its "most outspoken specimen" or (...)
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  39.  45
    Relational Dual Tableaux for Interval Temporal Logics.David Bresolin, Joanna Golinska-Pilarek & Ewa Orlowska - 2006 - Journal of Applied Non-Classical Logics 16 (3-4):251–277.
    Interval temporal logics provide both an insight into a nature of time and a framework for temporal reasoning in various areas of computer science. In this paper we present sound and complete relational proof systems in the style of dual tableaux for relational logics associated with modal logics of temporal intervals and we prove that the systems enable us to verify validity and entailment of these temporal logics. We show how to incorporate in the systems various relations between (...)
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  40.  3
    Holmes Rogers W.. Classical and Relational Logic. The Philosophical Review, Vol. 45 , Pp. 297–303.Charles A. Baylis - 1936 - Journal of Symbolic Logic 1 (2):69-69.
  41.  97
    The Relation Between Formal and Informal Logic.Ralph H. Johnson - 1999 - Argumentation 13 (3):265-274.
    The issue of the relationship between formal and informal logic depends strongly on how one understands these two designations. While there is very little disagreement about the nature of formal logic, the same is not true regarding informal logic, which is understood in various (often incompatible) ways by various thinkers. After reviewing some of the more prominent conceptions of informal logic, I will present my own, defend it and then show how informal logic, so understood, (...)
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  42. Indian Logic in the Early Schools: A Study of the Nyāyadarśana in its Relation to the Early Logic of Other Schools.H. N. Randle - 1930 - Munshiram Manoharlal Publishers.
     
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  43.  25
    Relational Semantics for the 4-Valued Relevant Logics BN4 and E4.Gemma Robles, José M. Blanco, Sandra M. López, Jesús R. Paradela & Marcos M. Recio - 2016 - Logic and Logical Philosophy 25 (2):173-201.
    The logic BN4 was defined by R.T. Brady in 1982. It can be considered as the 4-valued logic of the relevant conditional. E4 is a variant of BN4 that can be considered as the 4-valued logic of entailment. The aim of this paper is to define reduced general Routley-Meyer semantics for BN4 and E4. It is proved that BN4 and E4 are strongly sound and complete w.r.t. their respective semantics.
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  44.  25
    Independence Logic and Abstract Independence Relations.Gianluca Paolini - 2015 - Mathematical Logic Quarterly 61 (3):202-216.
    We continue the work on the relations between independence logic and the model-theoretic analysis of independence, generalizing the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a model-theoretic interpretation of the independence atom and characterize under which conditions we can prove a completeness result with respect to the deductive system that axiomatizes independence in team semantics and statistics.
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  45.  8
    Relational Approach for a Logic for Order of Magnitude Qualitative Reasoning with Negligibility, Non-Closeness and Distance.J. Golinska-Pilarek & E. Muñoz-Velasco - 2009 - Logic Journal of the IGPL 17 (4):375-394.
    We present a relational proof system in the style of dual tableaux for a multimodal propositional logic for order of magnitude qualitative reasoning to deal with relations of negligibility, non-closeness, and distance. This logic enables us to introduce the operation of qualitative sum for some classes of numbers. A relational formalization of the modal logic in question is introduced in this paper, i.e., we show how to construct a relational logic associated with the (...)
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  46.  35
    Relational Dual Tableau Decision Procedure for Modal Logic K.Joanna Golińska-Pilarek, Emilio Munoz-Velasco & Angel Mora - 2012 - Logic Journal of the IGPL 20 (4):747-756.
    We present a dual tableau system, RLK, which is itself a deterministic decision procedure verifying validity of K-formulas. The system is constructed in the framework of the original methodology of relational proof systems, determined only by axioms and inference rules, without any external techniques. Furthermore, we describe an implementation of the system RLK in Prolog, and we show some of its advantages.
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  47. Relevance Logics and Relation Algebras.Katalin Bimbó, J. Michael Dunn & Roger D. Maddux - 2009 - Review of Symbolic Logic 2 (1):102-131.
    Relevance logics are known to be sound and complete for relational semantics with a ternary accessibility relation. This paper investigates the problem of adequacy with respect to special kinds of dynamic semantics (i.e., proper relation algebras and relevant families of relations). We prove several soundness results here. We also prove the completeness of a certain positive fragment of R as well as of the first-degree fragment of relevance logics. These results show that some core ideas are shared between relevance (...)
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  48. The Relation of Logic to Ontology in Hegel.Paul Redding - 2012 - In Lila Haaparanta & Heikki Koskinen (eds.), Categories of Being: Essays on Metaphysics and Logic. Oxford University Press.
    Even among those philosophers who hold particular aspects of Hegel's philosophy in high regard, there have been few since the 19th century who have found Hegel's "metaphysics" plausible, and just as few not sceptical about the coherency of the "logical" project on which it is meant to be based. Indeed, against the type of work characteristic of the late nineteenth-century logical revolution which issued in modern analytic philosophy, it is often difficult to see exactly how Hegel's "logical" writings can be (...)
     
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  49.  39
    Relational Semantics for Kleene Logic and Action Logic.Katalin Bimbó & J. ~Michael Dunn - 2005 - Notre Dame Journal of Formal Logic 46 (4):461-490.
    Kleene algebras and action logic were proposed to be solutions to the finite axiomatization problem of the algebra of regular sets (of strings). They are treated here as nonclassical logics—with Hilbert-style axiomatizations and semantics. We also provide intuitive accounts in terms of information states of the semantics which provide further insights into the formalisms. The three types of "Kripke-style'' semantics which we define develop insights from gaggle theory, and from our four-valued and generalized Kripke semantics for the minimal substructural (...)
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  50. Logical Properties of Foundational Mereogeometrical Relations in Bio-Ontologies.Thomas Bittner - 2009 - Applied ontology 4 (2):109-138.
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