Prawitz, D.: 1965, Natural Deduction; A Proof-Theoretical Study, Stockholm Studies in Philosophy 3. Almqvist and Wiksell.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a header saying which modules it depends on. Thus the directory of modules associated with this paper contains parallel, and even incompatible, developments. If you type Load strengthening, the file 1 This distinction is already present in Gentzen [15] pp. 71 2, 116 7, 141, 216 7) and Prawitz [39] McKinnaPollack.tex; 7 12 1998; 17:47; p.4 Some Lambda Calculus and Type Theory Formalized 5 strengthening.l (which contains the proof of strengthening for PTS) will be loaded, preceeded by every module it depends on 2 . There are over 60 proof source files with extension .l 3 containing ....

Prawitz, D.: 1965, Natural Deduction; A Proof-Theoretical Study, Stockholm Studies in Philosophy 3. Almqvist and Wiksell.

....de ne all logical constants in terms of equality, at least from a classical point of view. We do things in an intuitionistic manner, giving useful deductive rules before we later assert the Law of the Excluded Middle, i.e. that every Boolean term is either true or false. While it is more typical (Prawitz 1965) to take a few additional logical constants such as 8 and ) as primitive, our approach is very similar to the usual de nitions of the internal logic of a topos; see e.g. Lambek and Scott (1986) We will now show how all the logical constants are de ned. These are (true) and) implies) 8 ....

....All the logical constants are de ned; we have seen the de nitions above. From the de nitions, rules for manipulating them directly are derived, so for most purposes users can forget that they aren t primitives. Most of the rules are so called introduction and elimination rules of natural deduction (Prawitz 1965). 1 For example, the introduction rule for conjunctions, CONJ, takes two theorems and gives a new theorem that results from conjoining ( anding ) them, e.g. #CONJ (REFL 1 ) ASSUME x = 2 ) it : thm = x = 2 (1 = 1) x = 2) Conversely, the elimination rules CONJUNCT1 and CONJUNCT2 ....

Prawitz, D. (1965) Natural deduction; a proof-theoretical study, Volume 3 of Stockholm Studies in Philosophy. Almqvist and Wiksells.

....all logical constants in terms of equality, at least from a classical point of view. We do things in an intuitionistic manner, giving useful deductive rules before we later assert the Law of the Excluded Middle, i.e. that every Boolean term is either true or false. While it is more typical (Prawitz 1965) to take a few additional logical constants such as 8 and ) as primitive, our approach is very similar to the usual definitions of the internal logic of a topos; see e.g. Lambek and Scott (1986) We will now show how all the logical constants are defined. These are (true) and) implies) ....

....the logical constants are defined; we have seen the definitions above. From the definitions, rules for manipulating them directly are derived, so for most purposes users can forget that they aren t primitives. Most of the rules are so called introduction and elimination rules of natural deduction (Prawitz 1965). 1 For example, the introduction rule for conjunctions, CONJ, takes two theorems and gives a new theorem that results from conjoining ( anding ) them, e.g. #CONJ (REFL 1 ) ASSUME x = 2 ) it : thm = x = 2 (1 = 1) x = 2) Conversely, the elimination rules CONJUNCT1 and CONJUNCT2 ....

Prawitz, D. (1965) Natural deduction; a proof-theoretical study, Volume 3 of Stockholm Studies in Philosophy. Almqvist and Wiksells.

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