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  1. J. C. Abbott (1976). Orthoimplication Algebras. Studia Logica 35 (2):173 - 177.
    Orthologic is defined by weakening the axioms and rules of inference of the classical propositional calculus. The resulting Lindenbaum-Tarski quotient algebra is an orthoimplication algebra which generalizes the author's implication algebra. The associated order structure is a semi-orthomodular lattice. The theory of orthomodular lattices is obtained by adjoining a falsity symbol to the underlying orthologic or a least element to the orthoimplication algebra.
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  2. Ernest W. Adams (1986). On the Logic of High Probability. Journal of Philosophical Logic 15 (3):255 - 279.
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  3. Stefano Aguzzoli, Matteo Bianchi & Vincenzo Marra (2009). A Temporal Semantics for Basic Logic. Studia Logica 92 (2):147 - 162.
    In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t -norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se . In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show that BL formulas (...)
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  4. Irving H. Anellis (2009). Russell and His Sources for Non-Classical Logics. Logica Universalis 3 (2):153-218.
    My purpose here is purely historical. It is not an attempt to resolve the question as to whether Russell did or did not countenance nonclassical logics, and if so, which nonclassical logics, and still less to demonstrate whether he himself contributed, in any manner, to the development of nonclassical logic. Rather, I want merely to explore and insofar as possible document, whether, and to what extent, if any, Russell interacted with the various, either the various candidates or their, ideas that (...)
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  5. G. Aldo Antonelli (2000). Book Review To Appear in the Bulletin of Symbolic Logic. [REVIEW] Bulletin of Symbolic Logic 6 (4):480-84.
    The emergence, over the last twenty years or so, of so-called “non-monotonic” logics represents one of the most significant developments both in logic and artificial intelligence. These logics were devised in order to represent defeasible reasoning, i.e., that kind of inference in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further evidence.
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  6. G. Aldo Antonelli (1999). A Directly Cautious Theory of Defeasible Consequence for Default Logic Via the Notion of General Extension. Artificial Intelligence 109 (1-2):71-109.
    This paper introduces a generalization of Reiter’s notion of “extension” for default logic. The main difference from the original version mainly lies in the way conflicts among defaults are handled: in particular, this notion of “general extension” allows defaults not explicitly triggered to pre-empt other defaults. A consequence of the adoption of such a notion of extension is that the collection of all the general extensions of a default theory turns out to have a nontrivial algebraic structure. This fact has (...)
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  7. G. Aldo Antonelli (1992). Revision Rules: An Investigation Into Non-Monotonic Inductive Definitions. Dissertation, University of Pittsburgh
    Many different modes of definition have been proposed over time, but none of them allows for circular definitions, since, according to the prevalent view, the term defined would then be lacking a precise signification. I argue that although circular definitions may at times fail uniquely to pick out a concept or an object, sense still can be made of them by using a rule of revision in the style adopted by Anil Gupta and Nuel Belnap in the theory of truth.
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  8. Ayda I. Arruda, R. Chuaqui & Newton C. A. Costdaa (eds.) (1980). Mathematical Logic in Latin America: Proceedings of the Iv Latin American Symposium on Mathematical Logic Held in Santiago, December 1978. Sole Distributors for the U.S.A. And Canada, Elsevier North-Holland.
    (or not oveA-complete.) . Let * be a unary operator defined on the set F of formulas of the language £ (ie, if A is a formula of £, then *A is also a ...
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  9. Charles Ashbacher (2002). Introduction to Neutrosophic Logic. American Research Press.
    Neutrosophic Logic was created by Florentin Smarandache (1995) and is an extension / combination of the fuzzy logic, intuitionistic logic, paraconsistent logic, ...
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  10. Arnon Avron, General Patterns for Nonmonotonic Reasoning: From Basic Entailments to Plausible Relations.
    This paper has two goals. First, we develop frameworks for logical systems which are able to re ect not only nonmonotonic patterns of reasoning, but also paraconsistent reasoning. Our second goal is to have a better understanding of the conditions that a useful relation for nonmonotonic reasoning should satisfy. For this we consider a sequence of generalizations of the pioneering works of Gabbay, Kraus, Lehmann, Magidor and Makinson. These generalizations allow the use of monotonic nonclassical logics as the underlying logic (...)
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  11. Diderik Batens (2007). A Universal Logic Approach to Adaptive Logics. Logica Universalis 1 (1):221-242.
    . In this paper, adaptive logics are studied from the viewpoint of universal logic (in the sense of the study of common structures of logics). The common structure of a large set of adaptive logics is described. It is shown that this structure determines the proof theory as well as the semantics of the adaptive logics, and moreover that most properties of the logics can be proved by relying solely on the structure, viz. without invoking any specific properties of the (...)
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  12. Diderik Batens (2000). Minimally Abnormal Models in Some Adaptive Logics. Synthese 125 (1-2):5-18.
    In an adaptive logic APL, based on a (monotonic) non-standardlogic PL the consequences of can be defined in terms ofa selection of the PL-models of . An important property ofthe adaptive logics ACLuN1, ACLuN2, ACLuNs1, andACLuNs2 logics is proved: whenever a model is not selected, this isjustified in terms of a selected model (Strong Reassurance). Theproperty fails for Priest's LP m because its way of measuring thedegree of abnormality of a model is incoherent – correcting thisdelivers the property.
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  13. Diderik Batens & Joke Meheus (2001). Shortcuts and Dynamic Marking in the Tableau Method for Adaptive Logics. Studia Logica 69 (2):221-248.
    Adaptive logics typically pertain to reasoning procedures for which there is no positive test. In [7], we presented a tableau method for two inconsistency-adaptive logics. In the present paper, we describe these methods and present several ways to increase their efficiency. This culminates in a dynamic marking procedure that indicates which branches have to be extended first, and thus guides one towards a decision — the conclusion follows or does not follow — in a very economical way.
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  14. Diderik Batens & Joke Meheus (2000). The Adaptive Logic of Compatibility. Studia Logica 66 (3):327-348.
    This paper describes the adaptive logic of compatibility and its dynamic proof theory. The results derive from insights in inconsistency-adaptive logic, but are themselves very simple and philosophically unobjectionable. In the absence of a positive test, dynamic proof theories lead, in the long run, to correct results and, in the short run, sometimes to final decisions but always to sensible estimates. The paper contains a new and natural kind of semantics for S5from which it follows that a specific subset of (...)
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  15. Edward Baŀuka (1965). On Verification of the Expressions of Many-Valued Sentential Calculi. I. Studia Logica 17 (1):53 - 73.
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  16. Jc Beall (2003). Algebraic Methods in Philosophical Logic. Australasian Journal of Philosophy 81 (3):442 – 444.
    Book Information Algebraic Methods in Philosophical Logic. By J. Michael Dunn and Gary Hardegree. Clarendon Press. Oxford. 2001. Pp. xv + 470. 60.50.
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  17. Jc Beall & David Ripley, Nonclassical Theories of Truth.
    This chapter attempts to give a brief overview of nonclassical (-logic) theories of truth. Due to space limitations, we follow a victory-through-sacrifice policy: sacrifice details in exchange for clarity of big-picture ideas. This policy results in our giving all-too-brief treatment to certain topics that have dominated discussion in the non-classical-logic area of truth studies. (This is particularly so of the ‘suitable conditoinal’ issue: §4.3.) Still, we present enough representative ideas that one may fruitfully turn from this essay to the more-detailed (...)
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  18. M. W. Bunder (1982). Deduction Theorems for Weak Implicational Logics. Studia Logica 41 (2-3):95 - 108.
    The standard deduction theorem or introduction rule for implication, for classical logic is also valid for intuitionistic logic, but just as with predicate logic, other rules of inference have to be restricted if the theorem is to hold for weaker implicational logics.In this paper we look in detail at special cases of the Gentzen rule for and show that various subsets of these in effect constitute deduction theorems determining all the theorems of many well known as well as not well (...)
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  19. Ricardo Caferra, Stéphane Demri & Michel Herment (1993). A Framework for the Transfer of Proofs, Lemmas and Strategies From Classical to Non Classical Logics. Studia Logica 52 (2):197 - 232.
    There exist valuable methods for theorem proving in non classical logics based on translation from these logics into first-order classical logic (abbreviated henceforth FOL). The key notion in these approaches istranslation from aSource Logic (henceforth abbreviated SL) to aTarget Logic (henceforth abbreviated TL). These methods are concerned with the problem offinding a proof in TL by translating a formula in SL, but they do not address the very important problem ofpresenting proofs in SL via a backward translation. We propose a (...)
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  20. Walter A. Carnielli, Marcelo E. Coniglio & Itala M. L. D'Ottaviano (2009). New Dimensions on Translations Between Logics. Logica Universalis 3 (1):1-18.
    After a brief promenade on the several notions of translations that appear in the literature, we concentrate on three paradigms of translations between logics: ( conservative ) translations , transfers and contextual translations . Though independent, such approaches are here compared and assessed against questions about the meaning of a translation and about comparative strength and extensibility of a logic with respect to another.
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  21. Gérard Chazal (2009). Logiques Non-Standard. Editions Universitaires de Dijon.
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  22. J. Delgrande & T. Schaub (eds.) (2004). Proceedings of NMR 2004. AAAI.
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  23. Fredrik Engström (2012). Generalized Quantifiers in Dependence Logic. Journal of Logic, Language and Information 21 (3):299-324.
    We introduce generalized quantifiers, as defined in Tarskian semantics by Mostowski and Lindström, in logics whose semantics is based on teams instead of assignments, e.g., IF-logic and Dependence logic. Both the monotone and the non-monotone case is considered. It is argued that to handle quantifier scope dependencies of generalized quantifiers in a satisfying way the dependence atom in Dependence logic is not well suited and that the multivalued dependence atom is a better choice. This atom is in fact definably equivalent (...)
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  24. Hartry Field, Harvey Lederman & Tore Fjetland Øgaard (forthcoming). Prospects for a Naive Theory of Classes. Notre Dame Journal of Formal Logic.
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  25. Branden Fitelson & Larry Wos (2001). Finding Missing Proofs with Automated Reasoning. Studia Logica 68 (3):329-356.
    This article features long-sought proofs with intriguing properties (such as the absence of double negation and the avoidance of lemmas that appeared to be indispensable), and it features the automated methods for finding them. The theorems of concern are taken from various areas of logic that include two-valued sentential (or propositional) calculus and infinite-valued sentential calculus. Many of the proofs (in effect) answer questions that had remained open for decades, questions focusing on axiomatic proofs. The approaches we take are of (...)
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  26. D. J. Foulis & S. Pulmannová (2012). Logical Connectives on Lattice Effect Algebras. Studia Logica 100 (6):1291-1315.
    An effect algebra is a partial algebraic structure, originally formulated as an algebraic base for unsharp quantum measurements. In this article we present an approach to the study of lattice effect algebras (LEAs) that emphasizes their structure as algebraic models for the semantics of (possibly) non-standard symbolic logics. This is accomplished by focusing on the interplay among conjunction, implication, and negation connectives on LEAs, where the conjunction and implication connectives are related by a residuation law. Special cases of LEAs are (...)
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  27. Greg Frost-Arnold (2008). Too Much Reference: Semantics for Multiply Signifying Terms. Journal of Philosophical Logic 37 (3):239 - 257.
    The logic of singular terms that refer to nothing, such as ‘Santa Claus,’ has been studied extensively under the heading of free logic. The present essay examines expressions whose reference is defective in a different way: they signify more than one entity. The bulk of the effort aims to develop an acceptable formal semantics based upon an intuitive idea introduced informally by Hartry Field and discussed by Joseph Camp; the basic strategy is to use supervaluations. This idea, as it stands, (...)
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  28. André Fuhrmann & Edwin D. Mares (1994). On S. Studia Logica 53 (1):75 - 91.
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  29. Tomasz Furmanowski (1983). The Logic of Algebraic Rules as a Generalization of Equational Logic. Studia Logica 42 (2-3):251 - 257.
    In this paper we start an investigation of a logic called the logic of algebraic rules. The relation of derivability of this logic is defined on universal closures of special disjunctions of equations extending the relation of derivability of the usual equational logic. The paper contains some simple theorems and examples given in justification for the introduction of our logic. A number of open questions is posed.
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  30. Dov M. Gabbay (1993). Classical Vs Non-Classical Logics: The Universality of Classical Logic. Max-Planck-Institut für Informatik.
  31. Joanna Golinska-Pilarek (2007). Rasiowa-Sikorski Proof System for the Non-Fregean Sentential Logic SCI. Journal of Applied Non-Classical Logics 17 (4):509–517.
    The non-Fregean logic SCI is obtained from the classical sentential calculus by adding a new identity connective = and axioms which say ?a = ß' means ?a is identical to ß'. We present complete and sound proof system for SCI in the style of Rasiowa-Sikorski. It provides a natural deduction-style method of reasoning for the non-Fregean sentential logic SCI.
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  32. Joanna Golinska-Pilarek (2006). Number of Non-Fregean Sentential Logics That Have Adequate Models. Mathematical Logic Quarterly 52 (5):439–443.
    We show that there are continuum many different non-Fregean sentential logics that have adequate models. The proof is based on the construction of a special class of models of the power of the continuum.
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  33. Joanna Golińska-Pilarek & Taneli Huuskonen (2012). Logic. Of Descriptions. A New Approach to the Foundations of Mathematics and Science. Studies in Logic, Grammar and Rhetoric 27:63-94.
    We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and complete- ness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems.
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  34. Joanna Golińska-Pilarek & Taneli Huuskonen (2005). Number of Extensions of Non-Fregean Logics. Journal of Philosophical Logic 34 (2):193 - 206.
    We show that there are continuum many different extensions of SCI (the basic theory of non-Fregean propositional logic) that lie below WF (the Fregean extension) and are closed under substitution. Moreover, continuum many of them are independent from WB (the Boolean extension), continuum many lie above WB and are independent from WH (the Boolean extension with only two values for the equality relation), and only countably many lie between WH and WF.
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  35. Lloyd Humberstone (2000). An Intriguing Logic with Two Implicational Connectives. Notre Dame Journal of Formal Logic 41 (1):1-40.
    Matthew Spinks [35] introduces implicative BCSK-algebras, expanding implicative BCK-algebras with an additional binary operation. Subdirectly irreducible implicative BCSK-algebras can be viewed as flat posets with two operations coinciding only in the 1- and 2-element cases, each, in the latter case, giving the two-valued implication truth-function. We introduce the resulting logic (for the general case) in terms of matrix methodology in §1, showing how to reformulate the matrix semantics as a Kripke-style possible worlds semantics, thereby displaying the distinction between the two (...)
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  36. Makoto Kanazawa (1992). The Lambek Calculus Enriched with Additional Connectives. Journal of Logic, Language and Information 1 (2):141-171.
    Some formal properties of enriched systems of Lambek calculus with analogues of conjunction and disjunction are investigated. In particular, it is proved that the class of languages recognizable by the Lambek calculus with added intersective conjunction properly includes the class of finite intersections of context-free languages.
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  37. Srećko Kovač (2012). Modal Collapse in Gödel's Ontological Proof. In Miroslaw Szatkowski (ed.), Ontological Proofs Today. Ontos Verlag. 50--323.
    After introductory reminder of and comments on Gödel’s ontological proof, we discuss the collapse of modalities, which is provable in Gödel’s ontological system GO. We argue that Gödel’s texts confirm modal collapse as intended consequence of his ontological system. Further, we aim to show that modal collapse properly fits into Gödel’s philosophical views, especially into his ontology of separation and union of force and fact, as well as into his cosmological theory of the nonobjectivity of the lapse of time. As (...)
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  38. Robert A. Kowalski & Francesca Toni (1996). Abstract Argumentation. Artificial Intelligence and Law 4 (3-4):275-296.
    In this paper we explore the thesis that the role of argumentation in practical reasoning in general and legal reasoning in particular is to justify the use of defeasible rules to derive a conclusion in preference to the use of other defeasible rules to derive a conflicting conclusion. The defeasibility of rules is expressed by means of non-provability claims as additional conditions of the rules.We outline an abstract approach to defeasible reasoning and argumentation which includes many existing formalisms, including default (...)
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  39. Bert Leuridan (2009). Causal Discovery and the Problem of Ignorance. An Adaptive Logic Approach. Journal of Applied Logic 7 (2):188-205.
    In this paper, I want to substantiate three related claims regarding causal discovery from non-experimental data. Firstly, in scientific practice, the problem of ignorance is ubiquitous, persistent, and far-reaching. Intuitively, the problem of ignorance bears upon the following situation. A set of random variables V is studied but only partly tested for (conditional) independencies; i.e. for some variables A and B it is not known whether they are (conditionally) independent. Secondly, Judea Pearl’s most meritorious and influential algorithm for causal discovery (...)
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  40. Bert Leuridan (2007). Supervenience: Its Logic and its Inferential Role in Classical Genetics. Logique Et Analyse 198:147-171.
  41. 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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  42. Adam Morton (1975). Complex Individuals and Multigrade Relations. Noûs 9 (3):309-318.
    I relate plural quantification, and predicate logic where predicates do not need a fixed number of argument places, to the part-whole relation. For more on these themes see later work by Boolos, Lewis, and Oliver & Smiley.
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  43. Charles Parsons (1966). A Propositional Calculus Intermediate Between the Minimal Calculus and the Classical. Notre Dame Journal of Formal Logic 7 (4):353-358.
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  44. W. A. Pogorzelski & J. Słupecki (1960). Basic Properties of Deductive Systems Based on Nonclassical Logics. Part II. Studia Logica 10 (1):94-95.
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  45. Erich Rast (2010). Classical Possibilism and Fictional Objects. In Franck Lihoreau (ed.), Fiction in Philosophy.
    An account of non-existing objects called 'classical possibilism', according to which objects that don't actually exist do exist in various other ways, is implemented in a two-dimensional modal logic with non-traditional predication theory. This account is very similar to Priest's, but preserves bivalence and does not endorse dialethism. The power of classical possibilism is illustrated by giving some examples that makes use of a description theory of reference. However, the same effect could also be achieved in a more Millian fashion. (...)
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  46. Greg Restall, And Negations.
    interesting. In this paper, we combine nonclassical logics of negation and possibility in the presence of conjunction and disjunction, and then we combine the resulting systems with intuitionistic logic. We will nd that Kracht's results on the undecidability of classical modal logics generalise to a non-classical setting. We will also see conditions under which intuitionistic logic can be combined with a non-intuitionistic negation without corrupting the intuitionistic fragment of the logic.
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  47. Peter Roeper (2004). First- and Second-Order Logic of Mass Terms. Journal of Philosophical Logic 33 (3):261-297.
    Provided here is an account, both syntactic and semantic, of first-order and monadic second-order quantification theory for domains that may be non-atomic. Although the rules of inference largely parallel those of classical logic, there are important differences in connection with the identification of argument places and the significance of the identity relation.
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  48. Joshua Schechter (2011). Juxtaposition: A New Way to Combine Logics. Review of Symbolic Logic 4 (4):560-606.
    This paper develops a new framework for combining propositional logics, called "juxtaposition". Several general metalogical theorems are proved concerning the combination of logics by juxtaposition. In particular, it is shown that under reasonable conditions, juxtaposition preserves strong soundness. Under reasonable conditions, the juxtaposition of two consequence relations is a conservative extension of each of them. A general strong completeness result is proved. The paper then examines the philosophically important case of the combination of classical and intuitionist logics. Particular attention is (...)
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  49. Beverley Skeggs (1997). Formations of Class and Gender: Becoming Respectable. Sage.
    Explanations of how identity is constructed are fundamental to contemporary debates in feminism and social theory. In this important addition to the literature, Beverley Skeggs demonstrates that class needs to be featured more prominently in theoretical accounts of gender, identity, and power. Class has been marginalized in feminist and cultural theory and it has become increasingly difficult to teach, research, or speak about class. Formations of Class and Gender identifies the neglect of class issues in favor of gender issues, and (...)
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  50. Philippe Smets (ed.) (1988). Non-Standard Logics for Automated Reasoning. Academic Press.
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