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Aristotle's Syllogistic and Core Logic
2014
History and Philosophy of Logic
The syllogisms in all four figures are re-proved in the binary system, and are thereby revealed as all on a par with each other. ...
First I regiment the syllogisms in the Gentzen-Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations ofAristotle's ...
Introduction rules and parallelized elimination rules for the new binary quantifiers in a system of natural deduction In order for Qx(ϕ, ψ) (Q = A, E, I, O) to be a sentence, both ϕ and ψ must have x as ...
doi:10.1080/01445340.2013.867144
fatcat:tcoeg5zyhvbhlekuk3a76hgnxu
Beyond binaries : a way forward for comparativeeducation
2012
Revista Española de Educación Comparada
We can think of each of these binaries at opposite ends of a set of spectrums. ...
, inductive-deductive, and practice-theory. ...
Inductive reasoning contrasts with deductive reasoning in that a general conclusion is arrived at by specific examples. ...
doi:10.5944/reec.20.2012.7596
fatcat:gkyavavvkbgdtappwqaasbyqlq
Cognitive Binary Logic - The Natural Unified Formal Theory of Propositional Binary Logic
2011
arXiv
pre-print
It is also shown here that Cognitive Binary Logic is a self-described theory in which the Liar Paradox is deconstructed. ...
This paper presents a formal theory which describes propositional binary logic as a semantically closed formal language, and allows for syntactically and semantically well-formed formulae, formal proofs ...
Gentzen's natural deduction system (sequent calculus) [1] , completeness [6] , consistency (soundness) [6] -all of them considered in the context of propositional binary logic, equivalence relations ...
arXiv:1106.2352v1
fatcat:neib2lzwfbdvzhve4pn2cxp3pq
Correspondence analysis for strong three-valued logic
2014
Logical Investigations
Second, I define a class of natural deduction systems on the basis of these charac- terizing basic inference schemes and a natural deduction system for K3. ...
Third, I show that each of the resulting natural deduction systems is sound and complete with respect to its particular semantics. ...
Third, I define a class of natural deduction systems on the basis of these characterizing inference schemes and a natural deduction system for K 3 . ...
doi:10.21146/2074-1472-2014-20-0-253-266
fatcat:re4yictcqnca7dat5xf26oz7by
Page 36 of Mathematical Reviews Vol. , Issue 90A
[page]
1990
Mathematical Reviews
No. 7 (1975), 7-13; MR 51 #2877] into sequence- conclusion natural deduction systems. ...
Logic 14 (1985), no. 4, 359-377; MR 87e:03148] the author introduced a type of natural deduction systems, which he calls “sequence-conclusion natural deduction”, where deductions are trees having in each ...
COMPLETENESS VIA CORRESPONDENCE FOR EXTENSIONS OF THE LOGIC OF PARADOX
2012
The Review of Symbolic Logic
Second, we define a class of natural deduction systems on the basis of these characterizing inference schemes and a natural deduction system for L P. ...
Third, we show that each of the resulting natural deduction systems is sound and complete with respect to its particular semantics. ...
Second, we define a class of natural deduction systems on the basis of a natural deduction system for L P and the 9 plus 27 characterizing inference schemes. ...
doi:10.1017/s1755020312000196
fatcat:vcwwfbk3rbdv7dx5vwc6vc533e
Deductive Systems in Traditional and Modern Logic
2020
Axioms
Since its inception, logic has studied the acceptable rules of reasoning, the rules that allow us to pass from certain statements, serving as premises or assumptions, to a statement taken as a conclusion ...
with a new binary connective that expresses the identity of two statements. ...
In [8] , A. Citkin studies the deductive systems with multiple conclusion rules which admit the introduction of meta-disjunction. ...
doi:10.3390/axioms9030108
fatcat:hviq34mlgracri3qdsawrwfopi
A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation
2019
Bulletin of the Section of Logic
This paper presents a way of formalising definite descriptions with a binary quantifier ℩, where ℩x[F, G] is read as 'The F is G'. ...
Procedures for removing maximal formulas of the form ℩x[F, G] are given, and it is shown that deductions in the system can be brought into normal form. ...
In this paper, I investigate the binary quantifier ι in the context of a system of natural deduction for intuitionist negative free logic. ...
doi:10.18778/0138-0680.48.2.01
fatcat:2b2dzoljqbggrdb2cj25xd7x5u
On the Paths of Categories
[chapter]
2015
Advances in Proof-Theoretic Semantics
To determine what deductions are it does not seem sufficient to know that the premises and conclusions are propositions, or something in the field of propositions, like commands and questions. ...
It seems equally, if not more, important to know that deductions make structures, which in mathematics we find in categories, multicategories and polycategories. ...
Acknowledgments Work on this paper was supported by the Ministry of Education, Science and Technological Development of Serbia, while the Alexander von Humboldt Foundation has supported the presentation of a ...
doi:10.1007/978-3-319-22686-6_4
fatcat:bzf54fgdezhh3m757aehulegua
Page 4595 of Mathematical Reviews Vol. , Issue 2000g
[page]
2000
Mathematical Reviews
Summary: “We provide a natural extension of the intuitionis- tic natural deduction system NJ with at most two consequences, which we call a binary-conclusion natural deduction (BCN) sys- tem. ...
Wim Ruitenburg (1-MRQT; Milwaukee, WI)
2000g:03021 03B20 03B10
Fujita, Ken-Etsu (J-K YUIT-AI; Iizuka)
A binary-conclusion natural deduction system. (English summary) Log. J. ...
Definite Descriptions in Intuitionist Positive Free Logic
2020
Logic and Logical Philosophy
The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. ...
This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. ...
Two referees for this journal also made helpful comments on a previous version. Its final version was prepared while I was an Alexander von Humboldt fellow at the University of Bochum. ...
doi:10.12775/llp.2020.024
fatcat:db42dyll4vgfdbs6hsx2ze7q34
A deductive database based on aristotelian logic
1989
Journal of symbolic computation
with a prototype system. ...
The paper proposes a new type of deductive database, whose structure is based on Aristotle's rules of the syllogism. ...
Note that the system in section 7.1 is also, by this definition, a natural deduction system. ...
doi:10.1016/s0747-7171(89)80030-6
fatcat:5ful6qwsozcljpmjau3d3a63by
Existence and Identity in Free Logic: A Problem for Inferentialism?
2007
Mind
First, it argues that the method of natural deduction idealizes the essential details of correct informal deductive reasoning. ...
The final part of the investigation brings out an underlying order in a basic family of free logics. ...
For whatever reasonable system of free logic one chooses, there is a natural-deduction system for it, and the rules of inference involved ought to be 'capturing' the meanings of the logical operators involved ...
doi:10.1093/mind/fzm1055
fatcat:y2pwpc44fzhkllc3w54ojlmwr4
A Decision Support System with Artificial Intelligence and Natural Language Processing to Mitigate the Deduction Rate of Health Insurance Claims
2021
Applied Sciences
A natural language method—latent Dirichlet allocation (LDA), was used to analyze patients' medical records. ...
The ratio of the deducted weight to the total weight claimed by a hospital is defined as the health insurance claim deduction rate (HICDR). ...
Summaries: obtain empirical conclusions problem/topic; • Storage sub-system: develop a data lake [22] to store the evidence. ...
doi:10.3390/app112411623
fatcat:t2a7xegb35f2jgggn7jeaamth4
R2
1971
Proceedings of the May 18-20, 1971, spring joint computer conference on - AFIPS '71 (Spring)
For information concerning these systems we refer the reader to Simmons. 13 ,14 Of the more advanced question-answering systems Green and Raphael 6 ,7 have developed a very powerful deductive procedure ...
A good way to study natural language man-machine communication is through the development, of question-answering systems; for it is in these systems that a well-defined natural language discourse takes ...
CONCLUSION The R2 system described in this paper exhibits a number of advanced features not found in existing natural language question-answering systems. ...
doi:10.1145/1478786.1478829
dblp:conf/afips/BissCS71
fatcat:mij6jjjrqner5h2db6hxpwferq
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