Mathematical Interpretation of Formal Systems

1957 ◽  
Vol 41 (336) ◽  
pp. 158
Author(s):  
R. L. Goodstein ◽  
Th. Skolem ◽  
G. Hasenjaeger ◽  
G. Kreisel ◽  
A. Robinson ◽  
...  
Keyword(s):  
Formal Systems ◽  
Mathematical Interpretation

G. Kreisel. On the concepts of completeness and interpretation of formal systems. Fundamenta mathematicae, vol. 39 (for 1952, pub. 1953), pp. 103–127. - G. Kreisel. Applications of mathematical logic to various branches of mathematics. Applications scientifiques de la logique mathématique, Actes du 2e Colloque International de Logique Mathématique, Paris — 25–30 août 1952, Institut Henri Poincaré, Collection de logique mathématique, ser. A no. 5, lithographed (“dactyl-spécial”), Gauthier-Villars, Paris 1954, and E. Nauwelaerts, Louvain 1954, pp. 37–49. - A. Robinson and G. Kreisel. Discussion. Applications scientifiques de la logique mathématique, Actes du 2e Colloque International de Logique Mathématique, Paris — 25–30 août 1952, Institut Henri Poincaré, Collection de logique mathématique, ser. A no. 5, lithographed (“dactyl-spécial”), Gauthier-Villars, Paris 1954, and E. Nauwelaerts, Louvain 1954, p. 50. - G. Kreisel. Models, translations, and interpretations. Mathematical interpretation of formal systems, Studies in logic and the foundations of mathematics, North-Holland Publishing Company, Amsterdam1955, pp. 26–50.

1959 ◽  
Vol 24 (3) ◽  
pp. 236-238
Author(s):  
William Craig
Keyword(s):  
Mathematical Logic ◽  
Publishing Company ◽  
Foundations Of Mathematics ◽  
Henri Poincaré ◽  
North Holland Publishing Company ◽  
Formal Systems ◽  
North Holland Publishing ◽  
Systems Studies ◽  
Mathematical Interpretation

Aristotle's syllogistic and modern logic

2005 ◽  
Vol 48 (3-4) ◽  
pp. 155-166
Author(s):  
Danica Andjelkovic
Keyword(s):  
Boolean Algebra ◽  
Predicate Calculus ◽  
Logical Theory ◽  
Modern Logic ◽  
Formal Systems ◽  
Mathematical Interpretation

Different understandings of Aristotle's syllogistic as a logical theory are reviewed. Leibniz offered a mathematical interpretation of syllogistic. Boole expressed all syllogistic relations by means of algebraic formulas. Lukasiewicz built a system of syllogistic as a logical theory separate and different from the predicate calculus Comparing syllogistic with other formal systems, its definitional equivalence with Boolean algebra is proven. Many systems of syllogistic are built, and their differences are due to recognizing the bearer of existential sense of categorical propositions. It is shown that these systems can be embedded in the predicate calculus, which means that syllogistic is not a separate and different theory from the predicate calculus.

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