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  1. Les attitudes russelliennes.Fabien Schang - 2017 - Cahiers de Philosophie de L’Université de Caen 54:149-168.
    Russell prétend qu’un examen des croyances est indispensable pour définir nos raisonnements quotidiens et comprendre ce que les philosophes entendent par la notion de vérité. Cela étant, l’auteur considère qu’une étude de ces croyances n’a aucun rapport avec la logique, laquelle concerne uniquement le vrai et le faux. En d’autres termes, Russell associe croyance et psychologie tout en réservant le domaine de la logique au thème de la proposition, vraie ou fausse par définition. Une certaine théorie de la vérité sous-tend (...)
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  2. Logical Inquiries Into a New Formal System with Plural Reference.Ran Lanzet & Hanoch Ben-Yami - 2004 - In Vincent Hendricks, Fabian Neuhaus, Stig Andur Pedersen, Uwe Schefler & Wansing Heinrich (eds.), First-Order Logic Revisited. Berlin: Logos Verlag. pp. 173-223.
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  3. Strong Normalization via Natural Ordinal.Daniel Durante Pereira Alves - 1999 - Dissertation,
    The main objective of this PhD Thesis is to present a method of obtaining strong normalization via natural ordinal, which is applicable to natural deduction systems and typed lambda calculus. The method includes (a) the definition of a numerical assignment that associates each derivation (or lambda term) to a natural number and (b) the proof that this assignment decreases with reductions of maximal formulas (or redex). Besides, because the numerical assignment used coincide with the length of a specific sequence of (...)
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  4. Sistema Experto para Resolver Problemas Lógicos de Deducción.Gabriel Garduño-Soto, David René Thierry García, Rafael Vidal Uribe & Hugo Padilla Chacón - 1989 - In Va. Conferencia Internacional: Las Computadoras en Instituciones de Educación y de Investigación. Cómputo Académico, UNAM, UNISYS, México, noviembre 14–16, 1989. Mexico City, México: National Autonomous University of Mexico.
    Proceeding of the first public presentation of the work of the mexican logical group "Deduktor" under the direction of the mexican professor Hugo Padilla Chacón. This work was in fact the first whole and stand alone arithmetization of logics.
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  5. I Exist.Cosmin Visan - 2015 - Journal of Consciousness Exploration & Research 6 (3):185-193.
    Why is there something rather than nothing? This is probably the most profound question that can be asked. In this paper, a rather unexpected simple solution is provided. The solution comes from analysing the truth value of the proposition “I exist.” It will be shown that this proposition is always true, so our existence is a logical necessity. Speculations about the implications over the universe as a whole are then provided.
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  6. Probabilities on Sentences in an Expressive Logic.Marcus Hutter, John W. Lloyd, Kee Siong Ng & William T. B. Uther - 2013 - Journal of Applied Logic 11 (4):386-420.
    Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being (...)
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  7. LOGIC TEACHING IN THE 21ST CENTURY.John Corcoran - 2016 - Quadripartita Ratio: Revista de Argumentación y Retórica 1 (1):1-34.
    We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, observationalism, (...)
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  8. Carnap’s Theory of Descriptions and its Problems.Jan Heylen - 2010 - Studia Logica 94 (3):355-380.
    Carnap's theory of descriptions was restricted in two ways. First, the descriptive conditions had to be non-modal. Second, only primitive predicates or the identity predicate could be used to predicate something of the descriptum. The motivating reasons for these two restrictions that can be found in the literature will be critically discussed. Both restrictions can be relaxed, but Carnap's theory can still be blamed for not dealing adequately with improper descriptions.
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  9. METAPHYSICAL RELATIVITY THEORY I: M-LOGIC.Eric Hahn - manuscript
    The present text provides a logical theory which originated in the unification of a number of well-known philosophical logics as well as the introduction and study of new operators. Further M-logic contains an object theory. With both the logical part and the object part we achieve a formal calculus that is able to express many metaphysical dogmas.
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  10. Subregular Tetrahedra.John Corcoran - 2008 - Bulletin of Symbolic Logic 14 (3):411-2.
    This largely expository lecture deals with aspects of traditional solid geometry suitable for applications in logic courses. Polygons are plane or two-dimensional; the simplest are triangles. Polyhedra [or polyhedrons] are solid or three-dimensional; the simplest are tetrahedra [or triangular pyramids, made of four triangles]. -/- A regular polygon has equal sides and equal angles. A polyhedron having congruent faces and congruent [polyhedral] angles is not called regular, as some might expect; rather they are said to be subregular—a word coined for (...)
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  11. Logically Equivalent False Universal Propositions with Different Counterexample Sets.John Corcoran - 2007 - Bulletin of Symbolic Logic 11:554-5.
    This paper corrects a mistake I saw students make but I have yet to see in print. The mistake is thinking that logically equivalent propositions have the same counterexamples—always. Of course, it is often the case that logically equivalent propositions have the same counterexamples: “every number that is prime is odd” has the same counterexamples as “every number that is not odd is not prime”. The set of numbers satisfying “prime but not odd” is the same as the set of (...)
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  12. Un acercamiento preliminar a la semántica fregeana.Esteban J. Beltrán Ulate - 2013 - INVENIO 31:23-31.
    El artículo no pretende ser estudio detallado de la semántica de Gottlob Frege, más bien, se caracteriza por ser un acercamiento a la distinción entre signo (Zeichen), representaciones (Vortellungen), sentido (Sinn) y referencia (Bedeutung) expuesta por el autor. La argumentación fregeana discute la manera desde la cual se puede referir, a través de signos, y como, de éstos, emerge un mundo (tercer mundo), de sentido, que puede estar o no ligado a una referencia. El presente estudio recurre a dos obras (...)
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  13. Free Logics Their Foundations, Character and Some Applications Thereof.Karel Lambert - 1997
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  14. Compositionality and Modest Inferentialism.James Trafford - 2014 - Teorema: International Journal of Philosophy (1):39-56.
    This paper provides both a solution and a problem for the account of compositionality in Christopher Peacocke’s modest inferentialism. The immediate issue facing Peacocke’s account is that it looks as if compositionality can only be understood at the level of semantics, which is difficult to reconcile with inferentialism. Here, following up a brief suggestion by Peacocke, I provide a formal framework wherein compositionality occurs the level of the determining relation between inference and semantics. This, in turn provides a “test” for (...)
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  15. Completeness and Correspondence in Chellas–Segerberg Semantics.Matthias Unterhuber & Gerhard Schurz - 2014 - Studia Logica 102 (4):891-911.
    We investigate a lattice of conditional logics described by a Kripke type semantics, which was suggested by Chellas and Segerberg – Chellas–Segerberg (CS) semantics – plus 30 further principles. We (i) present a non-trivial frame-based completeness result, (ii) a translation procedure which gives one corresponding trivial frame conditions for arbitrary formula schemata, and (iii) non-trivial frame conditions in CS semantics which correspond to the 30 principles.
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  16. Modulated Logics and Flexible Reasoning.Walter Carnielli & Maria Cláudia C. Grácio - 2008 - Logic and Logical Philosophy 17 (3):211-249.
    This paper studies a family of monotonic extensions of first-order logic which we call modulated logics, constructed by extending classical logic through generalized quantifiers called modulated quantifiers. This approach offers a new regard to what we call flexible reasoning. A uniform treatment of modulated logics is given here, obtaining some general results in model theory. Besides reviewing the “Logic of Ultrafilters”, which formalizes inductive assertions of the kind “almost all”, two new monotonic logical systems are proposed here, the “Logic of (...)
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  17. XVI Brazilian Logic Conference (EBL 2011).Walter Carnielli, Renata de Freitas & Petrucio Viana - 2012 - Bulletin of Symbolic Logic 18 (1):150-151.
    This is the report on the XVI BRAZILIAN LOGIC CONFERENCE (EBL 2011) held in Petrópolis, Rio de Janeiro, Brazil between May 9–13, 2011 published in The Bulletin of Symbolic Logic Volume 18, Number 1, March 2012. -/- The 16th Brazilian Logic Conference (EBL 2011) was held in Petro ́polis, from May 9th to 13th, 2011, at the Laboratório Nacional de Computação o Científica (LNCC). It was the sixteenth in a series of conferences that started in 1977 with the aim of (...)
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  18. Quine l’extensionaliste. Entre naturalisme et esthétisme.Fabien Schang - 2005 - Philosophia Scientiae 9 (2):279-293.
    La position résolument extensionaliste de Quine a été appuyée par des arguments de nature différente, dans ses multiples articles destinés à rejeter le projet de logique modale. On peut classer ces arguments en trois catégories : un argument naturaliste, où l’auteur tente de baser le langage scientifique sur une notation tâchée de décrire la “structure ultime de la réalité” ; un argument esthétique, où Quine fait allusion à des raisons de clarté et d’efficacité démonstrative pour privilégier la théorie des fonctions (...)
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  19. What is Nominalistic Mereology?Jeremy Meyers - 2012 - Journal of Philosophical Logic (DOI 10.1007/S10992-012-9252-4) (1):1-38.
    Abstract Hybrid languages are introduced in order to evaluate the strength of “minimal” mereologies with relatively strong frame definability properties. Appealing to a robust form of nominalism, I claim that one investigated language Hm is maximally acceptable for nominalistic mereology. In an extension Hgem of Hm, a modal analog for the classical systems of Leonard and Goodman (J Symb Log 5:45–55, 1940) and Lesniewski (1916) is introduced and shown to be complete with respect to 0- deleted Boolean algebras. We characterize (...)
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  20. The Master Argument of Diodorus Cronus.Ludger Jansen - 2011 - In Michael Bruce & Steven Barbone (eds.), Just the Arguments: 100 of the Most Important Arguments in Western Philosophy. Wiley-Blackwell.
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  21. An Analytic Tableau System for Natural Logic.Reinhard Muskens - 2010 - In Maria Aloni, H. Bastiaanse, T. De Jager & Katrin Schulz (eds.), Logic, Language and Meaning. Springer. pp. 104-113.
    Logic has its roots in the study of valid argument, but while traditional logicians worked with natural language directly, modern approaches first translate natural arguments into an artificial language. The reason for this step is that some artificial languages now have very well developed inferential systems. There is no doubt that this is a great advantage in general, but for the study of natural reasoning it is a drawback that the original linguistic forms get lost in translation. An alternative approach (...)
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  22. What the Prophet and the Philosopher Told Their Nations: A Multi-Modal Systems View of Norms and Civilisation.J. D. R. de Raadt - 1996 - World Futures 47 (1):53-67.
    (1996). What the prophet and the philosopher told their nations: A multi‐modal systems view of norms and civilisation. World Futures: Vol. 47, Unity and Diversity in Contemporary Systems Tinking: Systematic Pictures at an Exhibition, pp. 53-67.
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  23. Models for Modal Syllogisms.Fred Johnson - 1989 - Notre Dame Journal of Formal Logic 30 (2):271-284.
    A semantics is presented for Storrs McCall's separate axiomatizations of Aristotle's accepted and rejected polysyllogisms. The polysyllogisms under discussion are made up of either assertoric or apodeictic propositions. The semantics is given by associating a property with a pair of sets: one set consists of things having the property essentially and the other of things having it accidentally. A completeness proof and a semantic decision procedure are given.
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  24. Topological Aspects of Combinatorial Possibility.Thomas Mormann - 1997 - Logic and Logical Philosophy 5:75 - 92.
    The aim of this paper is to show that topology has a bearing on<br><br>combinatorial theories of possibility. The approach developed in this article is “mapping account” considering combinatorial worlds as mappings from individuals to properties. Topological structures are used to define constraints on the mappings thereby characterizing the “really possible” combinations. The mapping approach avoids the well-known incompatibility problems. Moreover, it is compatible with atomistic as well as with non-atomistic ontologies.It helps to elucidate the positions of logical atomism and monism (...)
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  25. Reflexivity: A Source-Book in Self-Reference.Steven James Bartlett (ed.) - 1992 - Distributors for the U.S. And Canada, Elsevier Science Pub. Co..
    From the Editor’s Introduction: "The Internal Limitations of Human Understanding." We carry, unavoidably, the limits of our understanding with us. We are perpetually confined within the horizons of our conceptual structure. When this structure grows or expands, the breadth of our comprehensions enlarges, but we are forever barred from the wished-for glimpse beyond its boundaries, no matter how hard we try, no matter how much credence we invest in the substance of our learning and mist of speculation. -/- The limitations (...)
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  26. The Consistency Argument for Ranking Functions.Franz Huber - 2007 - Studia Logica 86 (2):299-329.
    The paper provides an argument for the thesis that an agent’s degrees of disbelief should obey the ranking calculus. This Consistency Argument is based on the Consistency Theorem. The latter says that an agent’s belief set is and will always be consistent and deductively closed iff her degrees of entrenchment satisfy the ranking axioms and are updated according to the ranktheoretic update rules.
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  27. Categorial Grammar and Lexical-Functional Grammar.Reinhard Muskens - 2001 - In Miriam Butt & Tracey Holloway King (eds.), Proceedings of the LFG01 Conference, University of Hong Kong. Stanford, CA: CSLI Publications. pp. 259-279.
    This paper introduces λ-grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, λ-grammars are multi-dimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure λ-terms in which each abstractor binds exactly one variable. Mathematically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the method seems more practicable.
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  28. Logic and the Sachverhalt.Barry Smith - 1989 - The Monist 72 (1):52-69.
    Those who conceive logic as a science have generally favoured one of two alternative conceptions as to what the subject-matter of this science ought to be. On the one hand is the nowadays somewhat old-fashioned-seeming view of logic as the science of judgment, or of thinking or reasoning activities in general. On the other hand is the view of logic as a science of ideal meanings, 'thoughts', or 'propositions in themselves'. There is, however, a third alternative conception, which enjoyed only (...)
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  29. Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic.Richard Zach - 1999 - Bulletin of Symbolic Logic 5 (3):331-366.
    Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...)
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Classical Logic
  1. What is a Paraconsistent Logic?Damian Szmuc, Federico Pailos & Eduardo Barrio - 2018 - In Jacek Malinowski & Walter Carnielli (eds.), Contradictions, From Consistency to Inconsistency. Springer Verlag.
    Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic is (...)
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  2. A Recovery Operator for Nontransitive Approaches.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - forthcoming - Review of Symbolic Logic:1-25.
    In some recent papers, Cobreros, Egré, Ripley and van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a non-transitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut (...)
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  3. Substructural Logics, Pluralism and Collapse.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - forthcoming - Synthese:1-17.
    When discussing Logical Pluralism several critics argue that such an open-minded position is untenable. The key to this conclusion is that, given a number of widely accepted assumptions, the pluralist view collapses into Logical Monism. In this paper we show that the arguments usually employed to arrive at this conclusion do not work. The main reason for this is the existence of certain substructural logics which have the same set of valid inferences as Classical Logic—although they are, in a clear (...)
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  4. Rumfitt on Truth-Grounds, Negation, and Vagueness.Richard Zach - 2018 - Philosophical Studies 175 (8):2079-2089.
    In The Boundary Stones of Thought, Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project.
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  5. Iffication, Preiffication, Qualiffication, Reiffication, and Deiffication.John Corcoran - 2008 - Bulletin of Symbolic Logic 14 (4):435-6.
    Iffication, Preiffication, Qualiffication, Reiffication, and Deiffication. -/- Roughly, iffication is the speech-act in which—by appending a suitable if-clause—the speaker qualifies a previous statement. The clause following if is called the qualiffication. In many cases, the intention is to retract part of the previous statement—called the preiffication. I can retract part of “I will buy three” by appending “if I have money”. This initial study focuses on logical relations among propositional contents of speech-acts—not their full conversational implicatures, which will be treated (...)
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  6. INFORMATION-THEORETIC LOGIC.John Corcoran - 1998 - In C. Martínez U. Rivas & L. Villegas-Forero (eds.), Truth in Perspective edited by C. Martínez, U. Rivas, L. Villegas-Forero, Ashgate Publishing Limited, Aldershot, England (1998) 113-135. ASHGATE. pp. 113-135.
    Information-theoretic approaches to formal logic analyse the "common intuitive" concept of propositional implication (or argumental validity) in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; an argument is valid if the conclusion contains no information beyond that of the premise-set. This paper locates information-theoretic approaches historically, philosophically and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and (...)
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  7. SEPTEMBER 2015 UPDATE CORCORAN ARISTOTLE BIBLIOGRAPHY.John Corcoran - forthcoming - Aporia 5.
    This presentation includes a complete bibliography of John Corcoran’s publications relevant on Aristotle’s logic. The Sections I, II, III, and IV list respectively 23 articles, 44 abstracts, 3 books, and 11 reviews. Section I starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article—from Corcoran’s Philadelphia period that antedates his discovery of Aristotle’s natural deduction system—and the Journal of Symbolic Logic article—from his Buffalo period first reporting his original results. It ends with works published in 2015. (...)
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  8. Surprises in Logic.John Corcoran & William Frank - 2013 - Bulletin of Symbolic Logic 19 (3):253.
    JOHN CORCORAN AND WILIAM FRANK. Surprises in logic. Bulletin of Symbolic Logic. 19 253. Some people, not just beginning students, are at first surprised to learn that the proposition “If zero is odd, then zero is not odd” is not self-contradictory. Some people are surprised to find out that there are logically equivalent false universal propositions that have no counterexamples in common, i. e., that no counterexample for one is a counterexample for the other. Some people would be surprised to (...)
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  9. Expressing Set-Size Equality.John Corcoran & Gerald Rising - 2015 - Bulletin of Symbolic Logic 21 (2):239.
    The word ‘equality’ often requires disambiguation, which is provided by context or by an explicit modifier. For each sort of magnitude, there is at least one sense of ‘equals’ with its correlated senses of ‘is greater than’ and ‘is less than’. Given any two magnitudes of the same sort—two line segments, two plane figures, two solids, two time intervals, two temperature intervals, two amounts of money in a single currency, and the like—the one equals the other or the one is (...)
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  10. Second-Order Logic.John Corcoran - 2001 - In M. Zeleny (ed.), Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. KLUKER. pp. 61–76.
    “Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of our traditional intuitive logical framework and (...)
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  11. CORCORAN'S 27 ENTRIES IN THE 1999 SECOND EDITION.John Corcoran - 1999 - In Robert Audi (ed.), The Cambridge Dictionary of Philosophy. CAMBRIDGE UP. pp. 65-941.
    Corcoran’s 27 entries in the 1999 second edition of Robert Audi’s Cambridge Dictionary of Philosophy [Cambridge: Cambridge UP]. -/- ancestral, axiomatic method, borderline case, categoricity, Church (Alonzo), conditional, convention T, converse (outer and inner), corresponding conditional, degenerate case, domain, De Morgan, ellipsis, laws of thought, limiting case, logical form, logical subject, material adequacy, mathematical analysis, omega, proof by recursion, recursive function theory, scheme, scope, Tarski (Alfred), tautology, universe of discourse. -/- The entire work is available online free at more than (...)
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  12. Compositionality and Modest Inferentialism.James Trafford - 2014 - Teorema: International Journal of Philosophy (1):39-56.
    This paper provides both a solution and a problem for the account of compositionality in Christopher Peacocke’s modest inferentialism. The immediate issue facing Peacocke’s account is that it looks as if compositionality can only be understood at the level of semantics, which is difficult to reconcile with inferentialism. Here, following up a brief suggestion by Peacocke, I provide a formal framework wherein compositionality occurs the level of the determining relation between inference and semantics. This, in turn provides a “test” for (...)
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  13. Aristotle's Modal Syllogisms.Fred Johnson - 2004 - In Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the History of Logic. Elsevier. pp. 1--247.
    McCall's system for contingent syllogisms is modified. A semantics for the resulting system is provided.
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  14. What Are Logical Notions?John Corcoran & Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
    In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.
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  15. Extended Gergonne Syllogisms.Fred Johnson - 1997 - Journal of Philosophical Logic 26 (5):553-567.
    Syllogisms with or without negative terms are studied by using Gergonne's ideas. Soundness, completeness, and decidability results are given.
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  16. Three-Membered Domains for Aristotle's Syllogistic.Fred Johnson - 1991 - Studia Logica 50 (2):181 - 187.
    The paper shows that for any invalid polysyllogism there is a procedure for constructing a model with a domain with exactly three members and an interpretation that assigns non-empty, non-universal subsets of the domain to terms such that the model invalidates the polysyllogism.
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  17. Intensional Models for the Theory of Types.Reinhard Muskens - 2007 - Journal of Symbolic Logic 72 (1):98-118.
    In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it (...)
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Aristotelian Logic
  1. An Arithmetization of Logical Oppositions.Fabien Schang - 2016 - In Jean-Yves Beziau & Gianfranco Basti (eds.), The Square of Opposition: A Cornerstone of Thought. Bâle, Suisse: pp. 215-237.
    An arithmetic theory of oppositions is devised by comparing expressions, Boolean bitstrings, and integers. This leads to a set of correspondences between three domains of investigation, namely: logic, geometry, and arithmetic. The structural properties of each area are investigated in turn, before justifying the procedure as a whole. Io finish, I show how this helps to improve the logical calculus of oppositions, through the consideration of corresponding operations between integers.
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  2. Aristotle's Logic.Paul The Persian - 2016 - Tehran: Parsi Anjoman.
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  3. Review of Shukri B. Abed, Aristotelian Logic and Arabic Language in Alfārābī.Hossein Ziai - 1991 - International Journal of Middle Eastern Studies 24 (4):708-711..
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  4. A Critical Examination of Ibn-Sina’s Theory of the Conditional Syllogism.Zia Movahed - 2009 - Sophia Perennis 1:5-22.
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