4 slides/page
... • epistemic logic: for reasoning about knowledge The simplest logic (on which all the rest are based) is propositional logic. It is intended to capture features of arguments such as the following: Borogroves are mimsy whenever it is brillig. It is now brillig and this thing is a borogrove. Hence thi ...
... • epistemic logic: for reasoning about knowledge The simplest logic (on which all the rest are based) is propositional logic. It is intended to capture features of arguments such as the following: Borogroves are mimsy whenever it is brillig. It is now brillig and this thing is a borogrove. Hence thi ...
Dependent Types In Lambda Cube
... be seen as a product type, which consists of types A and B, which themselves are again formulas on the side of logic, and types on the side of type theory. ◦ connective and type constructor: We could see already one example above, namely for conjunction connective. In the similar manner we can creat ...
... be seen as a product type, which consists of types A and B, which themselves are again formulas on the side of logic, and types on the side of type theory. ◦ connective and type constructor: We could see already one example above, namely for conjunction connective. In the similar manner we can creat ...
.pdf
... enters into some true proposition, and the substitution of Q for P wherever it appears results in a new proposition that is likewise true, and if this can be done for every proposition, then P and Q are said to be the same and conversely, if P and Q are the same, they can be substituted for one an ...
... enters into some true proposition, and the substitution of Q for P wherever it appears results in a new proposition that is likewise true, and if this can be done for every proposition, then P and Q are said to be the same and conversely, if P and Q are the same, they can be substituted for one an ...
PDF
... • Initially, Gentzen invented the sequent system to analyze the other deductive system he introduced: natural deduction. In fact, sequents can be thought of as abbreviated forms of natural deductions, where the left hand side stands for assumptions (leaves), and right hand side the conclusion (root) ...
... • Initially, Gentzen invented the sequent system to analyze the other deductive system he introduced: natural deduction. In fact, sequents can be thought of as abbreviated forms of natural deductions, where the left hand side stands for assumptions (leaves), and right hand side the conclusion (root) ...
PB-503C Datasheet - Global Specialties
... pulsers. Each with 1 normally-open, 1 normallyclosed output. Each output sinks up to 250 mA Frequency Range: 0.1Hz to 100KHz, six ranges Output Voltage: 0 to + 10Vp-p into 50 Ω Load ...
... pulsers. Each with 1 normally-open, 1 normallyclosed output. Each output sinks up to 250 mA Frequency Range: 0.1Hz to 100KHz, six ranges Output Voltage: 0 to + 10Vp-p into 50 Ω Load ...
a first atempt to full descriptions of the new class
... CIDOC-CRM Exx Product Type Subclass of: E55 Type Superclass of: Scope note: ...
... CIDOC-CRM Exx Product Type Subclass of: E55 Type Superclass of: Scope note: ...
on fuzzy intuitionistic logic
... they m a y be t r u e 'in different ways'. By accepting different t r u t h values, we also break t h e true-false-dualism of classical logic. If we know t h e degree of t r u t h of a sentence we do not necessarily know t h e degree of falsehood of the sentence. In Fuzzy Intuitionistic Logic a half ...
... they m a y be t r u e 'in different ways'. By accepting different t r u t h values, we also break t h e true-false-dualism of classical logic. If we know t h e degree of t r u t h of a sentence we do not necessarily know t h e degree of falsehood of the sentence. In Fuzzy Intuitionistic Logic a half ...
.pdf
... notions of substitution as well as the first formalization of (1), called Leibniz. In Sect. 3, we introduce introduce logic LF, which includes Leibniz as an inference rule, and prove that F1 and LF have the same theorems. In Sect. 4, we give two other formulations of (1), Leibniz-FA (for Function App ...
... notions of substitution as well as the first formalization of (1), called Leibniz. In Sect. 3, we introduce introduce logic LF, which includes Leibniz as an inference rule, and prove that F1 and LF have the same theorems. In Sect. 4, we give two other formulations of (1), Leibniz-FA (for Function App ...
Homework 1
... (that is, if x12 = 8, x13 = 3, x22 = 6 and so on), then x11 = 9. Proof: Suppose x11 = 9. Then since square(1, 1) = square(2, 1) = square(2, 2) = square(2, 3), rule 4 tells us that none of x21 , x22 , nor x23 can be 9. Similarly, since x37 = 9, none of x27 , x28 , nor x29 can be 9. Thus by rule 2 (wi ...
... (that is, if x12 = 8, x13 = 3, x22 = 6 and so on), then x11 = 9. Proof: Suppose x11 = 9. Then since square(1, 1) = square(2, 1) = square(2, 2) = square(2, 3), rule 4 tells us that none of x21 , x22 , nor x23 can be 9. Similarly, since x37 = 9, none of x27 , x28 , nor x29 can be 9. Thus by rule 2 (wi ...
Breck, Hartline
... the toolbox to IMP. IMP has no functions, (procedures, routines, methods). It has no way to write a functional abstraction. This makes it pretty uninteresting as a programming language. So we will overcompensate and introduce a language with nothing but functional abstraction: the lambda calculus. T ...
... the toolbox to IMP. IMP has no functions, (procedures, routines, methods). It has no way to write a functional abstraction. This makes it pretty uninteresting as a programming language. So we will overcompensate and introduce a language with nothing but functional abstraction: the lambda calculus. T ...
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.