This category needs an editor. We encourage you to help if you are qualified.

# Propositional Logic

 Summary Propositional logic is the simpler of the two modern classical logics.  It ignores entirely the structure within propositions.  In classical propositional logic, molecular or compound propositions are built up from atomic propositions by means of the connectives, whose meaning is given by their truth tables.  The principle by which the meaning or truth conditions of compound propositions can be recovered by this "building up" process is known as compositionality.This leaf node is a sub-category of classical logic.  As such, non-standard propositional logics are not normally classified in this category—unless a comparison between classical logic and another logic is being drawn or one is reduced to the other—although restrictions of propositional logic in which nothing not a theorem in ordinary propositional logic is a theorem in the restriction do fit here.  Also appropriate here are modest extensions of propositional logic, provided that Boole's three laws of thought are not violated, viz. a proposition is either true or false, not neither, and not both.Meta-theoretical results for propositional logic are also generally classified as "proof theory," "model theory," "mathematical logic," etc.
 Key works See below.
 Introductions Because of the age of propositional logic there are literally hundreds of introductions to logic which cover this subject reasonably well.   Instructors will have their own favorites.In selecting a book for classroom use, I recommend checking one thing: how much meta-theory is included, so that the book is neither below nor above the level students can handle. Show all references
Related categories
Siblings:

 187 found Search inside: (import / add options)   Sort by: publication yearbook pricefirst authorviewingsaddition date
 1 — 100 / 187
1. Alexander Abian (1970). Completeness of the Generalized Propositional Calculus. Notre Dame Journal of Formal Logic 11 (4):449-452.

My bibliography

Export citation
2. Jarosław Achinger & Andrzej W. Jankowski (1986). On Decidable Consequence Operators. Studia Logica 45 (4):415 - 424.
The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.

My bibliography

Export citation
3. We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an ipmrovement of, in the sense that it has a kind of the subformula property and is a slight modification of. In this system the cut rule is eliminated. The second axiomatization is a classical conservative extension of basic propositional logic. Using these axiomatizations, we prove interpolation theorems for basic propositional logic.

My bibliography

Export citation
4. Alice Ambrose (1962). Fundamentals of Symbolic Logic. New York, Holt, Rinehart and Winston.
Remove from this list |

My bibliography

Export citation
5. Irving H. Anellis (2011). Peirce's Truth-Functional Analysis and the Origin of the Truth Table. History and Philosophy of Logic 33 (1):87 - 97.
We explore the technical details and historical evolution of Charles Peirce's articulation of a truth table in 1893, against the background of his investigation into the truth-functional analysis of propositions involving implication. In 1997, John Shosky discovered, on the verso of a page of the typed transcript of Bertrand Russell's 1912 lecture on ?The Philosophy of Logical Atomism? truth table matrices. The matrix for negation is Russell's, alongside of which is the matrix for material implication in the hand of Ludwig (...)

My bibliography

Export citation

My bibliography

Export citation
7. R. B. Angell (1962). A Propositional Logic with Subjunctive Conditionals. Journal of Symbolic Logic 27 (3):327-343.

My bibliography

Export citation
8. R. B. Angell (1960). The Sentential Calculus Using Rule of Inference Re. Journal of Symbolic Logic 25 (2):143 -.

My bibliography

Export citation
9. R. Bradshaw Angell (1960). Note on a Less Restricted Type of Rule of Inference. Mind 69 (274):253-255.

My bibliography

Export citation
10. Rani Lill Anjum (2012). What's Wrong with Logic? Argumentos 4 (8).

My bibliography

Export citation
11. Rani Lill Anjum (2008). Three Dogmas of 'If'. In A. Leirfall & T. Sandmel (eds.), Enhet i Mangfold. Unipub.
In this paper I argue that a truth functional account of conditional statements ‘if A then B’ not only is inadequate, but that it eliminates the very conditionality expressed by ‘if’. Focusing only on the truth-values of the statements ‘A’ and ‘B’ and different combinations of these, one is bound to miss out on the conditional relation expressed between them. But this is not a flaw only of truth functionality and the material conditional. All approaches that try to treat conditionals (...)

My bibliography

Export citation
12. Rani Lill Anjum (2007). The Logic of If' — or How to Philosophically Eliminate Conditional Relations. Sorites - A Digital Journal of Analytic Philosophy 19:51-57.
In this paper I present some of Robert N. McLaughlin's critique of a truth functional approach to conditionals as it appears in his book On the Logic of Ordinary Conditionals. Based on his criticism I argue that the basic principles of logic together amount to epistemological and metaphysical implications that can only be accepted from a logical atomist perspective. Attempts to account for conditional relations within this philosophical framework will necessarily fail. I thus argue that it is not truth functionality (...)

My bibliography

Export citation
13. O. Anshakov & S. Rychkov (1995). On Finite-Valued Propositional Logical Calculi. Notre Dame Journal of Formal Logic 36 (4):606-629.

My bibliography

Export citation
14. Lee C. Archie (1979). A Simple Defense of Material Implication. Notre Dame Journal of Formal Logic 20 (2):412-414.

My bibliography

Export citation
15. Robert L. Armstrong (1976). A Question About Incompleteness. Notre Dame Journal of Formal Logic 17 (2):295-296.

My bibliography

Export citation
16. E. J. Ashworth (1968). Propositional Logic in the Sixteenth and Early Seventeenth Centuries. Notre Dame Journal of Formal Logic 9 (2):179-192.

My bibliography

Export citation
17. Axel Arturo Barceló Aspeitia (2008). Patrones Inferenciales (Inferential Patterns). Crítica 40 (120):3 - 35.
El objetivo de este artículo es proponer un método de traducción de tablas de verdad a reglas de inferencia, para la lógica proposicional, que sea tan directo como el tradicional método inverso (de reglas a tablas). Este método, además, permitirá resolver de manera elegante el viejo problema, formulado originalmente por Prior en 1960, de determinar qué reglas de inferencia definen un conectivo. /// This article aims at setting forth a method to translate truth tables into inference rules, in propositional logic, (...)

My bibliography

Export citation
18. INTRODUCTION The main purpose of this work is to provide an English translation of and commentary on a recently published Arabic text dealing with conditional propositions and syllogisms. The text is that of Avicenna (Abu 'All ibn Sina, ...

My bibliography

Export citation
19. Arnon Avron (2005). A Non-Deterministic View on Non-Classical Negations. Studia Logica 80 (2-3):159 - 194.
We investigate two large families of logics, differing from each other by the treatment of negation. The logics in one of them are obtained from the positive fragment of classical logic (with or without a propositional constant ff for “the false”) by adding various standard Gentzen-type rules for negation. The logics in the other family are similarly obtained from LJ+, the positive fragment of intuitionistic logic (again, with or without ff). For all the systems, we provide simple semantics which is (...)

My bibliography

Export citation
20. John Bacon (1975). Elementary Symbolic Logic. Teaching Philosophy 1 (2):220-221.

My bibliography

Export citation
21. Robert B. Barrett & Alfred J. Stenner (1971). The Myth of the Exclusive Or'. Mind 80 (317):116-121.

My bibliography

Export citation
22. Alfred W. Benn (1907). Symbolic Logic (a Reply). Mind 16 (63):470-473.

My bibliography

Export citation
23. Remove from this list |

My bibliography

Export citation
24. Stephen L. Bloom & Roman Suszko (1972). Investigations Into the Sentential Calculus with Identity. Notre Dame Journal of Formal Logic 13 (3):289-308.

My bibliography

Export citation
25. Stephen L. Bloom & Roman Suszko (1971). Semantics for the Sentential Calculus with Identity. Studia Logica 28 (1):77 - 82.

My bibliography

Export citation
26. Ivan Boh (1966). Propositional Connectives, Supposition, and Consequence in Paul of Pergola. Notre Dame Journal of Formal Logic 7 (1):109-128.

My bibliography

Export citation
27. Ivan Boh (1962). Symbolic Logic. The Modern Schoolman 39 (3):277-281.

My bibliography

Export citation
28. Jean-François Bonnefon & Guy Politzer (2011). Pragmatics, Mental Models and One Paradox of the Material Conditional. Mind and Language 26 (2):141-155.
Most instantiations of the inference ‘y; so if x, y’ seem intuitively odd, a phenomenon known as one of the paradoxes of the material conditional. A common explanation of the oddity, endorsed by Mental Model theory, is based on the intuition that the conclusion of the inference throws away semantic information. We build on this explanation to identify two joint conditions under which the inference becomes acceptable: (a) the truth of x has bearings on the relevance of asserting y; and (...)

My bibliography

Export citation

My bibliography

Export citation
30. Karl Britton (1936). Epistemological Remarks on the Propositional Calculus. Analysis 3 (4):57 - 63.

My bibliography

Export citation
31. Daniel J. Bronstein (1942). A Correction to the Sentential Calculus of Tarski's Introduction to Logic. Journal of Symbolic Logic 7 (1):34.

My bibliography

Export citation
32. This is part two of a complete exposition of Logic, in which there is a radically new synthesis of Aristotelian-Scholastic Logic with modern Logic. Part II is the presentation of the theory of propositions. Simple, composite, atomic, compound, modal, and tensed propositions are all examined. Valid consequences and propositional logical identities are rigorously proven. Modal logic is rigorously defined and proven. This is the first work of Logic known to unite Aristotelian logic and modern logic using scholastic logic as the (...)

My bibliography

Export citation
33. M. W. Bunder & R. M. Rizkalla (2009). Proof-Finding Algorithms for Classical and Subclassical Propositional Logics. Notre Dame Journal of Formal Logic 50 (3):261-273.

My bibliography

Export citation
34. F. K. C. (1978). Lewis Carroll's Symbolic Logic. The Review of Metaphysics 31 (3):472-473.

My bibliography

Export citation
35. W. C. C. (1952). Book Review:Symbolic Logic C. I. Lewis, C. H. Langford. [REVIEW] Philosophy of Science 19 (2):180-.

My bibliography

Export citation
36. Xavier Caicedo Ferrer (1978). A Formal System for the Non-Theorems of the Propositional Calculus. Notre Dame Journal of Formal Logic 19 (1):147-151.

My bibliography

Export citation
37. Rudolf Carnap (1958). Introduction to Symbolic Logic and its Applications. New York, Dover Publications.
Clear, comprehensive, intermediate introduction to logical languages, applications of symbolic logic to physics, mathematics, biology.

My bibliography

Export citation
38. James D. Carney (1970). Introduction to Symbolic Logic. Englewood Cliffs, N.J.,Prentice-Hall.
Remove from this list |

My bibliography

Export citation
39. Hector-Neri Casta Neda (1976). Leibniz's Syllogistico-Propositional Calculus. Notre Dame Journal of Formal Logic 17 (4):481-500.

My bibliography

Export citation
40. Hector-Neri Castañeda (1990). Leibniz's Complete Propositional Logic. Topoi 9 (1):15-28.
I have shown (to my satisfaction) that Leibniz's final attempt at a generalized syllogistico-propositional calculus in the Generales Inquisitiones was pretty successful. The calculus includes the truth-table semantics for the propositional calculus. It contains an unorthodox view of conjunction. It offers a plethora of very important logical principles. These deserve to be called a set of fundamentals of logical form. Aside from some imprecisions and redundancies the system is a good systematization of propositional logic, its semantics, and a correct account (...)

My bibliography

Export citation
41. Anthony Pike Cavendish (1953). Introduction to Symbolic Logic. University Tutorial Press.
Remove from this list |

My bibliography

Export citation
42. Douglas Cenzer & Jeffrey B. Remmel (2006). Complexity, Decidability and Completeness. Journal of Symbolic Logic 71 (2):399 - 424.
We give resource bounded versions of the Completeness Theorem for propositional and predicate logic. For example, it is well known that every computable consistent propositional theory has a computable complete consistent extension. We show that, when length is measured relative to the binary representation of natural numbers and formulas, every polynomial time decidable propositional theory has an exponential time (EXPTIME) complete consistent extension whereas there is a nondeterministic polynomial time (NP) decidable theory which has no polynomial time complete consistent extension (...)

My bibliography

Export citation
43. This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4–9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.
Remove from this list |

My bibliography

Export citation
44. Alonzo Church (1984). A Bibliography of Symbolic Logic, 1666-1935. Association for Symbolic Logic.
Remove from this list |

My bibliography

Export citation
45. Joseph T. Clark (1952). The Sentential Calculus. Philosophical Studies of the American Catholic Philosophical Association 3:15-17.

My bibliography

Export citation
46. D. S. Clarke (1973). Deductive Logic. Carbondale,Southern Illinois University Press.
This introduction to the basic forms of deductive inference as evaluated by methods of modern symbolic logic is de­signed for sophomore-junior-level stu­dents ready to specialize in the study of deductive logic. It can be used also for an introductory logic course. The inde­pendence of many sections allows the instructor utmost flexibility. The text consists of eight chapters, the first six of which are designed to intro­duce the student to basic topics of sen­tence and predicate logic. The last two chapters extend (...)
Remove from this list |

My bibliography

Export citation
47. Brian Coffey (1948). Elements of Symbolic Logic. The Modern Schoolman 25 (3):198-202.

My bibliography

Export citation
48. William S. Cooper (1968). The Propositional Logic of Ordinary Discourse. Inquiry 11 (1-4):295 – 320.
The logical properties of the 'if-then' connective of ordinary English differ markedly from the logical properties of the material conditional of classical, two-valued logic. This becomes apparent upon examination of arguments in conversational English which involve (noncounterfactual) usages of if-then'. A nonclassical system of propositional logic is presented, whose conditional connective has logical properties approximating those of 'if-then'. This proposed system reduces, in a sense, to the classical logic. Moreover, because it is equivalent to a certain nonstandard three-valued logic, its (...)

My bibliography

Export citation
49. Irving M. Copi (1973/1968). Symbolic Logic. New York,Macmillan.
50. Irving M. Copi (1950). Book Review:Fundamentals of Symbolic Logic Alice Ambrose, Morris Lazerowitz. [REVIEW] Philosophy of Science 17 (2):199-.

My bibliography

Export citation
51. John Corcoran & Susan B. Wood (1973). The Switches "Paradox" and the Limits of Propositional Logic. Philosophy and Phenomenological Research 34 (1):102-108.

My bibliography

Export citation
52. René Cori (2000). Mathematical Logic: A Course with Exercises. Oxford University Press.
Logic forms the basis of mathematics and is a fundamental part of any mathematics course. This book provides students with a clear and accessible introduction to this important subject, using the concept of model as the main focus and covering a wide area of logic. The chapters of the book cover propositional calculus, boolean algebras, predicate calculus and completelness theorems with answeres to all of the excercises and the end of the volume. This is an ideal introduction to mathematics and (...)
Remove from this list |

My bibliography

Export citation
53. Robert H. Cowen (1970). A New Proof of the Compactness Theorem for Propositional Logic. Notre Dame Journal of Formal Logic 11 (1):79-80.

My bibliography

Export citation
54. Stephen Crain & Drew Khlentzos (2010). The Logic Instinct. Mind and Language 25 (1):30-65.
We present a series of arguments for logical nativism, focusing mainly on the meaning of disjunction in human languages. We propose that all human languages are logical in the sense that the meaning of linguistic expressions corresponding to disjunction (e.g. English or , Chinese huozhe, Japanese ka ) conform to the meaning of the logical operator in classical logic, inclusive- or . It is highly implausible, we argue, that children acquire the (logical) meaning of disjunction by observing how adults use (...)

My bibliography

Export citation
55. Marvin J. Croy (2010). Teaching the Practical Relevance of Propositional Logic. Teaching Philosophy 33 (3):253-270.
This article advances the view that propositional logic can and should be taught within general education logic courses in ways that emphasizes its practical usefulness, much beyond what commonly occurs in logic textbooks. Discussion and examples of this relevance include database searching, understanding structured documents, and integrating concepts of proof construction with argument analysis. The underlying rationale for this approach is shown to have import for questions concerning the design of logic courses, textbooks, and the general education curriculum, particularly the (...)

My bibliography

Export citation
56. Janusz Czelakowski (1985). Algebraic Aspects of Deduction Theorems. Studia Logica 44 (4):369 - 387.
The first known statements of the deduction theorems for the first-order predicate calculus and the classical sentential logic are due to Herbrand [8] and Tarski [14], respectively. The present paper contains an analysis of closure spaces associated with those sentential logics which admit various deduction theorems. For purely algebraic reasons it is convenient to view deduction theorems in a more general form: given a sentential logic C (identified with a structural consequence operation) in a sentential language I, a quite arbitrary (...)

My bibliography

Export citation
57. Janusz Czelakowski & Wiesław Dziobiak (1991). A Deduction Theorem Schema for Deductive Systems of Propositional Logics. Studia Logica 50 (3-4):385 - 390.
We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) L and p, A(p, q) s q.

My bibliography

Export citation
58. J. D. (1963). Fundamentals of Symbolic Logic. The Review of Metaphysics 16 (3):579-579.

My bibliography

Export citation

My bibliography

Export citation
60. René David & Karim Nour (2003). A Short Proof of the Strong Normalization of Classical Natural Deduction with Disjunction. Journal of Symbolic Logic 68 (4):1277-1288.
We give a direct, purely arithmetical and elementary proof of the strong normalization of the cut-elimination procedure for full (i.e., in presence of all the usual connectives) classical natural deduction.

My bibliography

Export citation
61. James Dickoff (1965). Symbolic Logic and Language. New York, Mcgraw-Hill.
Remove from this list |

My bibliography

Export citation
62. Randall R. Dipert (1981). Peirce's Propositional Logic. The Review of Metaphysics 34 (3):569 - 595.

My bibliography

Export citation
63. Kosta Došen (1981). A Reduction of Classical Propositional Logic to the Conjunction-Negation Fragment of an Intuitionistic Relevant Logic. Journal of Philosophical Logic 10 (4):399 - 408.

My bibliography

Export citation

My bibliography

Export citation
65. L. Eley (1972). Life-World Constitution of Propositional Logic and Elementary Predicate Logic. Philosophy and Phenomenological Research 32 (3):322-340.

My bibliography

Export citation

My bibliography

Export citation
67. Frederic B. Fitch (1952). Symbolic Logic. New York, Ronald Press Co..
Remove from this list |

My bibliography

Export citation
68. 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 (...)

My bibliography

Export citation
69. Robert J. Fogelin (1972). Austinian Ifs. Mind 81 (324):578-580.

My bibliography

Export citation
70. Jerome Frazee (1988). A New Symbolic Representation of the Basic Truth-Functions of the Propositional Calculus. History and Philosophy of Logic 9 (1):87-91.
As with mathematics, logic is easier to do if its symbols and their rules are better. In a graphic way, the logic symbols introduced in thís paper show their truth-table values, their composite truth-functions, and how to say them as either ?or? or ?if ? then? propositions. Simple rules make the converse, add or remove negations, and resolve propositions.

My bibliography

Export citation
71. Todd M. Furman (2008). Making Sense of the Truth Table for Conditional Statements. Teaching Philosophy 31 (2):179-184.
This essay provides an intuitive technique that illustrates why a conditional must be true when the antecedent is false and the consequent is either true or false. Other techniques for explaining the conditional’s truth table are unsatisfactory.

My bibliography

Export citation
72. Dov M. Gabbay (1993). Classical Vs Non-Classical Logics: The Universality of Classical Logic. Max-Planck-Institut für Informatik.
Remove from this list |

My bibliography

Export citation
73. Henri Galinon (2009). A Note on Generalized Functional Completeness in the Realm of Elementrary Logic. Bulletin of the Section of Logic 38 (1):1-9.
We can think of functional completeness in systems of propositional logic as a form of expressive completeness: while every logical constant in such system expresses a truth-function of finitely many arguments, functional completeness garantees that every truth-function of finitely many arguments can be expressed with the constants in the system. From this point of view, a functionnaly complete system of propositionnal logic can thus be seen as one where no logical constant is missing. Can a similar question be formulated for (...)

My bibliography

Export citation
74. Martin Gardner (1958/1968). Logic Machines, Diagrams and Boolean Algebra. New York, Dover Publications.
Remove from this list |

My bibliography

Export citation
75. James W. Garson (2010). Expressive Power and Incompleteness of Propositional Logics. Journal of Philosophical Logic 39 (2):159-171.
Natural deduction systems were motivated by the desire to define the meaning of each connective by specifying how it is introduced and eliminated from inference. In one sense, this attempt fails, for it is well known that propositional logic rules (however formulated) underdetermine the classical truth tables. Natural deduction rules are too weak to enforce the intended readings of the connectives; they allow non-standard models. Two reactions to this phenomenon appear in the literature. One is to try to restore the (...)

My bibliography

Export citation
76. Ronald Glass (1984). Understanding Symbolic Logic. Teaching Philosophy 7 (2):181-183.

My bibliography

Export citation
77. Gilberto Gomes (2009). Are Necessary and Sufficient Conditions Converse Relations? Australasian Journal of Philosophy 87 (3):375 – 387.
Claims that necessary and sufficient conditions are not converse relations are discussed, as well as the related claim that If A, then B is not equivalent to A only if B . The analysis of alleged counterexamples has shown, among other things, how necessary and sufficient conditions should be understood, especially in the case of causal conditions, and the importance of distinguishing sufficient-cause conditionals from necessary-cause conditionals. It is concluded that necessary and sufficient conditions, adequately interpreted, are converse relations in (...)

My bibliography

Export citation
78. Gilberto Gomes (2006). If A, Then B Too, but Only If C: A Reply to Varzi. Analysis 66 (290):157–161.

My bibliography

Export citation
79. William K. Goosens (1977). Elementary Applied Symbolic Logic. Teaching Philosophy 2 (1):80-81.

My bibliography

Export citation
80. William Gustason (1973). Elementary Symbolic Logic. New York,Holt, Rinehart and Winston.
Remove from this list |

My bibliography

Export citation
81. Theodore Hailperin (1984). Boole's Abandoned Propositional Logic. History and Philosophy of Logic 5 (1):39-48.
The approach used by Boole in Mathematical analysis of logic to develop propositional logic was based on the idea of ?cases? or ?conjunctures of circumstances?. But this was dropped in Laws of thought in favor of one which Boole considered to be more satisfactory, that of using the notion of ?time for which a proposition is true?. We show that, when suitable clarifications and corrections are made, the earlier approach? which accords with modern logic in eschewing the extraneous notion of (...)

My bibliography

Export citation
82. William H. Hanson (1991). Indicative Conditionals Are Truth-Functional. Mind 100 (1):53-72.

My bibliography

Export citation
83. J. H. Harris (1982). What's So Logical About the “Logical” Axioms? Studia Logica 41 (2-3):159 - 171.
Intuitionists and classical logicians use in common a large number of the logical axioms, even though they supposedly mean different things by the logical connectives and quantifiers — conquans for short. But Wittgenstein says The meaning of a word is its use in the language. We prove that in a definite sense the intuitionistic axioms do indeed characterize the logical conquans, both for the intuitionist and the classical logician.

My bibliography

Export citation
84. Bernard A. Hausman (1937). Symbolic Logic. Thought 12 (1):136-137.

My bibliography

Export citation
85. Leon Henkin (1949). Fragments of the Propositional Calculus. Journal of Symbolic Logic 14 (1):42-48.

My bibliography

Export citation
86. This is a basic logic text for first-time logic students. Custom-made texts from the chapters is an option as well. And there is a website to go with text too: http://www.poweroflogic.com/cgi/menu.cgi .

My bibliography

Export citation
87. G. E. Hughes (1957). The Independence of Axioms in the Propositional Calculus. Australasian Journal of Philosophy 35 (1):21 – 29.

My bibliography

Export citation
88. L. Humberstone & D. Makinson (2012). Intuitionistic Logic and Elementary Rules. Mind 120 (480):1035-1051.
The interplay of introduction and elimination rules for propositional connectives is often seen as suggesting a distinguished role for intuitionistic logic. We prove three formal results concerning intuitionistic propositional logic that bear on that perspective, and discuss their significance. First, for a range of connectives including both negation and the falsum, there are no classically or intuitionistically correct introduction rules. Second, irrespective of the choice of negation or the falsum as a primitive connective, classical and intuitionistic consequence satisfy exactly the (...)

My bibliography

Export citation
89. A. Iacona (2005). Rethinking Bivalence. Synthese 146 (3):283 - 302.
Classical logic rests on the assumption that there are two mutually exclusive and jointly exhaustive truth values. This assumption has always been surrounded by philosophical controversy. Doubts have been raised about its legitimacy, and hence about the legitimacy of classical logic. Usually, the assumption is stated in the form of a general principle, namely the principle that every proposition is either true or false. Then, the philosophical controversy is often framed in terms of the question whether every proposition is either (...)

My bibliography

Export citation
90. Nikolay Ivanov & Dimiter Vakarelov (2012). A System of Relational Syllogistic Incorporating Full Boolean Reasoning. Journal of Logic, Language and Information 21 (4):433-459.
We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: $$\begin{array}{ll}\mathbf{Some}\, a \,{\rm are} \,R-{\rm related}\, {\rm to}\, \mathbf{some} \,b;\\ \mathbf{Some}\, a \,{\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{some}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all} \,b.\end{array}$$ Such primitives formalize sentences from natural language like ‘ All students read some textbooks’. Here a, b denote arbitrary sets (of objects), and R denotes an (...)

My bibliography

Export citation
91. A. E. J. (1966). Symbolic Logic. The Review of Metaphysics 19 (4):808-808.

My bibliography

Export citation
92. Frank Jackson (1987). Conditionals. Blackwell.
A defense of material implication as implication.

My bibliography

Export citation
93. Frank Jackson (1979). On Assertion and Indicative Conditionals. Philosophical Review 88 (4):565-589.

My bibliography

Export citation
94. Stanisław Jaśkowski (1975). Three Contributions to the Two-Valued Propositional Calculus. Studia Logica 34 (1):121 - 132.
Three chapters contain the results independent of each other. In the first chapter I present a set of axioms for the propositional calculus which are shorter than the ones known so far, in the second one I give a method of defining all ternary connectives, in the third one, I prove that the probability of propositional functions is preserved under reversible substitutions.

My bibliography

Export citation
95. Stanisław Jaśkowski (1969). Propositional Calculus for Contradictory Deductive Systems. Studia Logica 24 (1):143 - 160.

My bibliography

Export citation
96. R. E. Jennings (1994). The Genealogy of Disjunction. Oxford University Press.
This is a comprehensive study of the English word 'or', and the logical operators variously proposed to present its meaning. Although there are indisputably disjunctive uses of or in English, it is a mistake to suppose that logical disjunction represents its core meaning. 'Or' is descended from the Anglo-Saxon word meaning second, a form which survives in such expressions as "every other day." Its disjunctive uses arise through metalinguistic applications of an intermediate adverbial meaning which is conjunctive rather than disjunctive (...)

My bibliography

Export citation

My bibliography

Export citation
98. Stig Kanger (1955). A Note on Partial Postulate Sets for Propositional Logic. Theoria 21 (2-3):99-104.

My bibliography

Export citation
99. Kevin C. Klement, Propositional Logic. Internet Encyclopedia of Philosophy.
Propositional logic, also known as sentential logic and statement logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements. In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that depend upon parts (...)