en>Wavelength: inserting 1 hyphen: —> "one-dimensional"—wikt:one-dimensional

2014-02-20T20:12:23Z

inserting 1 hyphen: —> "one-dimensional"—wikt:one-dimensional

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	~~'''Minimal logic'''~~, ~~or '''minimal calculus'''~~, is a [~~[Mathematical logic\|symbolic logic]] system originally developed by [[Ingebrigt Johansson]~~]. It is ~~a variant~~ of ~~[[intuitionistic logic]] that rejects not only~~ the [~~[classical logic\|classical~~]~~] [[law of excluded middle]] (as intuitionistic logic does)~~, but ~~also~~ the ~~[[principle of explosion]] (ex falso quodlibet)~~.		Cardsharp two is a brand new improved superlight and large sharp utility knife, dimension of a credit score score card. Present capabilities consist of stiffer, polypropylene physique and unique basic safety lock. Just a few ingenious folding operation metamorphosis the card in an tasteful pocket utility resource. Slimmer and lighter than an widespread knife. The additional prolonged [http://en.wiktionary.org/wiki/pocketknife balisong knives] stainless metallic surgical blade ensures for a longer interval lasting rust cost-free sharpness. 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	~~Just like intuitionistic logic~~, ~~minimal logic~~ can be ~~formulated in~~ a ~~language using →, ∧, ∨, ⊥ (~~[~~[logical implication\|implication~~]~~], [[logical conjunction\|conjunction]], [[logical disjunction\|disjunction]] and [[falsum]]) as~~ the ~~basic [[logical connective\|connectives]], treating ¬A~~ as an ~~abbreviation~~ for ~~(A → ⊥)~~. In ~~this language it is axiomatized by~~ the ~~positive fragment (i.e~~., ~~formulas using only →~~, ~~∧, ∨) of intuitionistic logic~~, with ~~no additional axioms or rules about ⊥~~. ~~Thus minimal logic is a subsystem of intuitionistic logic,~~ and it is ~~strictly weaker~~ as ~~it does not derive~~ the ~~ex falso quodlibet principle~~ <~~math~~>~~\neg A,A\vdash B~~<~~/math~~> ~~(however~~, ~~it derives its special~~ case <~~math~~>~~\neg A,A\vdash \neg B~~<~~/math~~>).

	~~Adding the ex falso axiom <math>\neg A\~~to~~(A\~~to ~~B)</math>~~ to ~~minimal logic results in intuitionistic logic~~, and ~~adding~~ the ~~double negation law~~ <~~math~~>~~\neg\neg A\to A~~<~~/math~~> to ~~minimal logic results~~ in ~~classical logic~~.

	~~Minimal logic is closely related~~ to ~~[[simply typed lambda calculus]] via~~ the ~~[[Curry~~-~~Howard isomorphism]], i~~.e. the ~~[[typing derivation]]s of simply typed lambda terms are isomorphic~~ to ~~[[natural deduction]] proofs in minimal logic~~.

	~~==References==~~
	* [[Ingebrigt Johansson\|Johansson, Ingebrigt]], 1936, "[http://~~www~~.~~numdam~~.~~org~~/~~numdam~~-~~bin~~/item?id=~~CM_1937__4__119_0 Der Minimalkalkul, ein reduzierter intuitionistischer Formalismus~~].~~" ''Compositio Mathematica'' '''4''', 119–136~~.

	~~{{Logic}}~~

	~~{{mathlogic-stub}}~~
	[~~[Category~~:~~Non~~-~~classical logic~~]]
	[~~[Category~~:~~Constructivism (mathematics)]]~~
	~~[[Category:Systems of formal logic]~~]

12.144.110.131: /* Calculation of the synchronous spectrum */

2013-12-26T17:07:49Z

Calculation of the synchronous spectrum

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	~~My name: Winfred Perdue~~<br>~~My age: 32 years old~~<br>~~Country: Italy~~<br>~~City: San Nicola Di Centola~~ <br>~~Post code: 84070~~<br>~~Street: Piazzetta Scalette Rubiani 2~~<br><br>~~Check out my blog:~~ [http://www.~~tipsofthedays~~.~~com~~/~~profile~~/~~stlus Cannondale mountain bike sizing~~.]		'''Minimal logic''', or '''minimal calculus''', is a [[Mathematical logic\|symbolic logic]] system originally developed by [[Ingebrigt Johansson]]. It is a variant of [[intuitionistic logic]] that rejects not only the [[classical logic\|classical]] [[law of excluded middle]] (as intuitionistic logic does), but also the [[principle of explosion]] (ex falso quodlibet).

			Just like intuitionistic logic, minimal logic can be formulated in a language using →, ∧, ∨, ⊥ ([[logical implication\|implication]], [[logical conjunction\|conjunction]], [[logical disjunction\|disjunction]] and [[falsum]]) as the basic [[logical connective\|connectives]], treating ¬A as an abbreviation for (A → ⊥). In this language it is axiomatized by the positive fragment (i.e., formulas using only →, ∧, ∨) of intuitionistic logic, with no additional axioms or rules about ⊥. Thus minimal logic is a subsystem of intuitionistic logic, and it is strictly weaker as it does not derive the ex falso quodlibet principle <math>\neg A,A\vdash B</math> (however, it derives its special case <math>\neg A,A\vdash \neg B</math>).

			Adding the ex falso axiom <math>\neg A\to(A\to B)</math> to minimal logic results in intuitionistic logic, and adding the double negation law <math>\neg\neg A\to A</math> to minimal logic results in classical logic.

			Minimal logic is closely related to [[simply typed lambda calculus]] via the [[Curry-Howard isomorphism]], i.e. the [[typing derivation]]s of simply typed lambda terms are isomorphic to [[natural deduction]] proofs in minimal logic.

			==References==
			* [[Ingebrigt Johansson\|Johansson, Ingebrigt]], 1936, "[http://www.numdam.org/numdam-bin/item?id=CM_1937__4__119_0 Der Minimalkalkul, ein reduzierter intuitionistischer Formalismus]." ''Compositio Mathematica'' '''4''', 119–136.

			{{Logic}}

			{{mathlogic-stub}}
			[[Category:Non-classical logic]]
			[[Category:Constructivism (mathematics)]]
			[[Category:Systems of formal logic]]

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2012-08-25T17:08:21Z

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My name: Winfred Perdue My age: 32 years old Country: Italy City: San Nicola Di Centola Post code: 84070 Street: Piazzetta Scalette Rubiani 2 Check out my blog: [http://www.tipsofthedays.com/profile/stlus Cannondale mountain bike sizing.]

Two-dimensional correlation analysis - Revision history

en>Wavelength: inserting 1 hyphen: —> "one-dimensional"—wikt:one-dimensional

12.144.110.131: /* Calculation of the synchronous spectrum */

en>Bibcode Bot: Adding 0 arxiv eprint(s), 5 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot