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THE ALGORITHMS FOR IMPROVING AND REORGANIZING NATURAL DEDUCTION PROOFS

100%
Pak K.
Studies in Logic, Grammar and Rhetoric
|
2010
|
issue 22(35)
95-112
EN
It can be observed in the course of analyzing nontrivial examples of natural deduction proofs, either declarative or procedural, that the proofs are often formulated in a chaotic way. Authors tend to create deductions which are correct for computers, but hardly readable for humans, as they believe that finding and removing inessential reasoning fragments, or shortening the proofs is not so important as long as the computer accepts the proof script. This article consists of two parts. In the first part, we present some types of unnecessary deductions and methods of reorganizing proof graphs in order to make them closer to good quality informal mathematical reasoning. In the second part, we describe tools implemented to solve the above-mentioned problems. Next, we demonstrate their usability by analysing statistical data drawn from the Mizar Mathematical Library.
2

To Prove the Evident: On the Inferential Role of Euclidean Diagrams

80%
Crippa D.
Teorie vědy (Theory of Science)
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2009
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vol. 31
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issue 2
101-112
EN
Diagrams have been rightly acknowledged to license inferences in Euclid's geometric practice. However, if on one hand purely visual proofs are to be found nowhere in the Elements, on the other, fully fledged proofs of diagrammatically evident statements are offered, as in El. I. 20: 'In any triangle the sum of two sides is greater than the third'. In this paper the author explains, taking as a starting point Kenneth Manders' analysis of Euclidean diagram, how exact and co-exact claims enter proposition I. 20. Then, he ultimately argues that this proposition serves broader explanatory purposes, enhancing control on diagram appearance.
3
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W kwestii dowodów na istnienie Boga i dowodu na jedyność Spinozjańskiej substancji

70%
Kąkol T.
Filo-Sofija
|
2012
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vol. 12
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issue 2(17)
83-100
EN
Abstract In this paper I analyze Spinozian ontological arguments for God’s existence from Ethica ordine geometrico demonstrata. I argue that the first proof suffers from circulus vitiosus, whereas the others have at least one non-obvious premise. I also consider P. Gut’s modification of the first proof, reported to me during the conference “The Philosophy of the 17th Century—Its Origins and Continuations” (Gdańsk, 16.06.2011). Meanwhile, I address D. Chlastawa’s remark that theorem 7 and 14 from Ethica… makes Spinoza’s theory inconsistent.
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