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Stephen Cook and Phuong Nguyen. Logical foundations of proof
Stephen Cook and Phuong Nguyen. Logical foundations of proof

Logic of Natural Language Semantics: Presuppositions and
Logic of Natural Language Semantics: Presuppositions and

... d. CIs are logically and compositionally independent of what is ‘said (in the favored sense)’, i.e. independent of the at-issue entailments. In this talk, I mainly present Potts (2005) that shows a range of different empirical phenomena such as expressive expressions, appositive nominals (ANs) or ap ...
Digital Logic Topics - Agricultural engineering
Digital Logic Topics - Agricultural engineering

We showed on Tuesday that Every relation in the arithmetical
We showed on Tuesday that Every relation in the arithmetical

Gödel`s Dialectica Interpretation
Gödel`s Dialectica Interpretation

Propositional logic
Propositional logic

Functional Programming and the Lambda Calculus
Functional Programming and the Lambda Calculus

... If E 1 ↔ E 2 (are interconvertable), then there exists an E such that E 1 → E and E 2 → E . “Reduction in any way can eventually produce the same result.” If E 1 → E 2 , and E 2 is is normal form, then there is a normal-order reduction of E 1 to E 2 . “Normal-order reduction will always produce a no ...
Compactness Theorem for First-Order Logic
Compactness Theorem for First-Order Logic

Intuitionistic Logic
Intuitionistic Logic

... Intuitionism is an approach to the philosophy of mathematics and to mathematical practice pioneered by L. E. J. Brouwer. The central thesis of intuitionism is that mathematics has as its subject matter mental mathematical constructions. If they were all finite, then classical reasoning would be adeq ...
predicate
predicate

... •  ⊨  holds iff for all models M and lookup tables l, whenever M ⊨l  holds for all  then M ⊨l  holds as well •  is satisfiable iff there is some model M and lookup table l such that M ⊨l  holds •  is valid iff M ⊨l  holds for all models M and lookup tables l ...
crooks
crooks

... Large pad-over-logic pad cells for bump-bond tests LVDS receiver and transmitter pad circuits Gray code counter for timestamp generation Clock generator (makes all sensor internal clocks from one external clock) Bunch train state machine Readout state machine Master controller (co-ordinates precedin ...
inputs: A, B, C
inputs: A, B, C

(A B) |– A
(A B) |– A

... Grundzüge der theoretischen Logik, in which they arrived at exactly this point: they had defined axioms and derivation rules of predicate logic (slightly distinct from the above), and formulated the problem of completeness. They raised a question whether such a proof calculus is complete in the sens ...
Discrete Computational Structures (CS 225) Definition of Formal Proof
Discrete Computational Structures (CS 225) Definition of Formal Proof

CMP1101 Electronics I
CMP1101 Electronics I

Large 2 digit BCD input 1/8 DIN display - Model BCD-2
Large 2 digit BCD input 1/8 DIN display - Model BCD-2

Proof Theory - Andrew.cmu.edu
Proof Theory - Andrew.cmu.edu

... I will assume the reader is familiar with the language of first-order logic. Contemporary logic textbooks often present formal calculi for first-order logic with a long list of axioms and a few simple rules, but these are generally not very convenient for modeling deductive arguments or studying the ...
MathsReview
MathsReview

... Associate Professor, SIS Maths Review Sept 27, 2013 ...
Lecture 3.1
Lecture 3.1

Lecture 3.1
Lecture 3.1

... James Joshi Associate Professor, SIS Lecture 3.1 September 14, 2010 ...
Lecture 3
Lecture 3

Mata Kuliah Tehnik Digital Jurusan Fisika FMIPA Univ. Jember
Mata Kuliah Tehnik Digital Jurusan Fisika FMIPA Univ. Jember

Logic  I Fall  2009 Problem  Set  5
Logic I Fall 2009 Problem Set 5

... Problem Set 5 In class I talked about SL being truth-functionally complete (TF-complete). For the problems below, use TLB’s definition of TF-completeness, according to which it is sets of connectives that are (or aren’t) TF-complete: Definition: A set of connectives is TF-complete iff a language with ...
Mathematical Logic
Mathematical Logic

... Abduction/Induction: given a theory T and an observation φ, find an explanation Γ such that T ∪ Γ |= φ Satisfiability Checking: given a set of formulae Γ, check whether there exists a model I such that I |= φ for all φ ∈ Γ? Model Checking: given a model I and a formula φ, check whether I|=φ Automate ...
.pdf
.pdf

... Substitution A|pB is the replacement of all occurrences of the variable p in A by the formula B. There are a few issues, however, that one needs to be aware of. Variables that are bound by a quantifier, must not be replaced, as this would change the meaning. ((∃p)(p⊃∼q))|qp should not result in ((∃p ...
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Curry–Howard correspondence



In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard. It is the link between logic and computation that is usually attributed to Curry and Howard, although the idea is related to the operational interpretation of intuitionistic logic given in various formulations by L. E. J. Brouwer, Arend Heyting and Andrey Kolmogorov (see Brouwer–Heyting–Kolmogorov interpretation) and Stephen Kleene (see Realizability). The relationship has been extended to include category theory as the three-way Curry–Howard–Lambek correspondence.
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