On the consistency of a three-valued logical calculus

Topoi ◽  
1984 ◽  
Vol 3 (1) ◽  
pp. 3-12 ◽  
Author(s):  
D. A. Bochvar
Keyword(s):  
Logical Calculus

A logical calculus of the ideas immanent in nervous activity

1943 ◽  
Vol 5 (4) ◽  
pp. 115-133 ◽  
Author(s):  
Warren S. McCulloch ◽  
Walter Pitts
Keyword(s):  
Nervous Activity ◽  
Logical Calculus

G. H. R. Parkinson. Introduction. Leibniz, Logical papers, A selection translated and edited with an introduction by G. H. R. Parkinson, Clarendon Press, Oxford1966, pp. ix–Ixv. - Gottfried Wilhelm Leibniz. From Of the art of combination (1666). English translation of a portion of 11 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 1–11. - Gottfried Wilhelm Leibniz. Elements of a calculus (April, 1679). English translation of 114 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 17–24. - Gottfried Wilhelm Leibniz. Rules from which a decision can be made, by means of numbers, about the validity of inferences and about the forms and moods of categorical syllogisms (April, 1679). English translation of 118 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 25–32. - Gottfried Wilhelm Leibniz. A specimen of the universal calculus (1679–86?). English translation of 111 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 33–39. - Gottfried Wilhelm Leibniz. Addenda to the specimen of the universal calculus (1679–86?). English translation of 111 (without the three concluding paragraphs from Couturat) by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 40–46. - Gottfried Wilhelm Leibniz. General inquiries about the analysis of concepts and of truths (1686). English translation of 129 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 47–87. - Gottfried Wilhelm Leibniz. The primary bases of a logical calculus (1 August 1690). English translation of 133 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 90–92. - Gottfried Wilhelm Leibniz. The bases of a logical calculus (2 August 1690). English translation of 134 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 93–94. - Gottfried Wilhelm Leibniz. An intensional account of immediate inference and the syllogism (‘Logical definitions’). English translation of 18 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 112–114. - Gottfried Wilhelm Leibniz. A paper on ‘some logical difficulties’ (after 1690). English translation of 13 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 115–121. - Gottfried Wilhelm Leibniz. A study in the plus-minus calculus (‘A not inelegant specimen of abstract proof’) (after 1690). English translation of 16 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 122–130. - Gottfried Wilhelm Leibniz. A study in the calculus of real addition (after 1690). English translation of 112 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 131–144.

1968 ◽  
Vol 33 (1) ◽  
pp. 139-140
Author(s):  
Alonzo Church
Keyword(s):  
English Translation ◽  
Gottfried Wilhelm Leibniz ◽  
Logical Calculus ◽  
Real Addition ◽  
Leibniz Rules

Reasoning about Durations

2020 ◽  
Vol 32 (11) ◽  
pp. 2103-2116
Author(s):  
Laura Jane Kelly ◽  
Sangeet Khemlani ◽  
P. N. Johnson-Laird
Keyword(s):  
Mental Models ◽  
Model Theory ◽  
Mental Model ◽  
Alternative Model ◽  
Alternative Procedure ◽  
Logical Calculus ◽  
Deliberative System ◽  
System 2 ◽  
System 1 ◽  
Formal Rules

A set of assertions is consistent provided they can all be true at the same time. Naive individuals could prove consistency using the formal rules of a logical calculus, but it calls for them to fail to prove the negation of one assertion from the remainder in the set. An alternative procedure is for them to use an intuitive system (System 1) to construct a mental model of all the assertions. The task should be easy in this case. However, some sets of consistent assertions have no intuitive models and call for a deliberative system (System 2) to construct an alternative model. Formal rules and mental models therefore make different predictions. We report three experiments that tested their respective merits. The participants assessed the consistency of temporal descriptions based on statements using “during” and “before.” They were more accurate for consistent problems with intuitive models than for those that called for deliberative models. There was no robust difference in accuracy between consistent and inconsistent problems. The results therefore corroborated the model theory.

A minimum calculus for logic

1944 ◽  
Vol 9 (4) ◽  
pp. 89-94 ◽  
Author(s):  
Frederic B. Fitch
Keyword(s):  
Truth Table ◽  
Additional Property ◽  
Basic Logic ◽  
Double Negation ◽  
Logical Calculus ◽  
Logical Calculi

A logical calculus will be presented which not only is a formulation of a “basic logic” in the sense of the writer's previous papers, but which has the additional property that no weaker calculus can be a formulation of a basic logic. A sort of minimum logical calculus is thus attained, which has nothing superfluous about it for achieving the purpose for which it is designed.In the case of some logical calculi the question can arise as to whether certain of the postulates are really logically valid and necessary. Sometimes a test is available, such as the truth-table test, enabling us to distinguish between logically valid sentences and others, but often no such test is available, especially where quantifiers are involved. Is or is not the axiom of infinity, for example, to be regarded as logically valid? Or is the principle of double negation really acceptable, even though it satisfies the truth-table test?

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