Chapter 5 - Stanford Lagunita
... from a conjunction of any number of sentences, any one of its conjuncts. This inference pattern is sometimes called conjunction elimination or simplification, when it is presented in the context of a formal system of deduction. When it is used in informal proofs, however, it usually goes by without ...
... from a conjunction of any number of sentences, any one of its conjuncts. This inference pattern is sometimes called conjunction elimination or simplification, when it is presented in the context of a formal system of deduction. When it is used in informal proofs, however, it usually goes by without ...
PREDICATE LOGIC
... bound is said to be free. Later, we will see that the same variable can occur both bound and free in an expression. For this reason, it is important to also indicate the position of the variable in question. Example 1.11. Find the bound and free variables in ∀ z (P (z) ∧ Q(x)) ∨ ∃ y Q(y). Solution: ...
... bound is said to be free. Later, we will see that the same variable can occur both bound and free in an expression. For this reason, it is important to also indicate the position of the variable in question. Example 1.11. Find the bound and free variables in ∀ z (P (z) ∧ Q(x)) ∨ ∃ y Q(y). Solution: ...
page 113 THE AGM THEORY AND INCONSISTENT BELIEF
... beliefs from implicit beliefs which are derived from the explicit beliefs, or separating relevant beliefs from irrelevant beliefs. Based on this approach, several formal techniques have been developed in recent years to deal with inconsistent beliefs; for example, Chopra and Parikh (2000), Hansson a ...
... beliefs from implicit beliefs which are derived from the explicit beliefs, or separating relevant beliefs from irrelevant beliefs. Based on this approach, several formal techniques have been developed in recent years to deal with inconsistent beliefs; for example, Chopra and Parikh (2000), Hansson a ...
Document
... Structural Induction (cont’d.) • To prove that every string x Expr satisfies a condition P(x), use structural induction: show that – P(a) is true – For every x and every y in Expr, if P(x) and P(y) are true, then P(x ◦ y) and P(x • y) are true – For every x Expr, if P(x) is true, then P(◊(x)) i ...
... Structural Induction (cont’d.) • To prove that every string x Expr satisfies a condition P(x), use structural induction: show that – P(a) is true – For every x and every y in Expr, if P(x) and P(y) are true, then P(x ◦ y) and P(x • y) are true – For every x Expr, if P(x) is true, then P(◊(x)) i ...
Lattice Presentation
... Routing Delays and Port Timings All synchronous blocks require specific Setup/Hold time (TSU/TH) on IN ports and they provide specific Clock To Out (TCO) on OUT ports. - These TSU/TH/TCO values are determined by simulation of the device, by characterization, or by ‘binning’ at final test. The ro ...
... Routing Delays and Port Timings All synchronous blocks require specific Setup/Hold time (TSU/TH) on IN ports and they provide specific Clock To Out (TCO) on OUT ports. - These TSU/TH/TCO values are determined by simulation of the device, by characterization, or by ‘binning’ at final test. The ro ...
01-Intro
... two wires both “1” - make another be “1” (AND) at least one of two wires “1” - make another be “1” (OR) a wire “1” - then make another be “0” (NOT) Memory devices (store) ...
... two wires both “1” - make another be “1” (AND) at least one of two wires “1” - make another be “1” (OR) a wire “1” - then make another be “0” (NOT) Memory devices (store) ...
A Nonstandard Approach to the. Logical Omniscience Problem
... where all the rules of standard logic hold. For example, a formula is valid exactly if it is true in all the standard worlds in every structure. The intuition here is that the nonstandard worlds serve only as epistemic alternatives; although an agent may be muddled and may consider a nonstandard wor ...
... where all the rules of standard logic hold. For example, a formula is valid exactly if it is true in all the standard worlds in every structure. The intuition here is that the nonstandard worlds serve only as epistemic alternatives; although an agent may be muddled and may consider a nonstandard wor ...
A retrospective on Haskell
... Less mundanely (but more allusively) sexy types let you think higher thoughts and still stay [almost] sane: ...
... Less mundanely (but more allusively) sexy types let you think higher thoughts and still stay [almost] sane: ...
Functional Programming
... • We can formally model the process of evaluating an expression as the application of one or more reduction rules. • E.g., lambda-calculus includes the beta-reduction rule to evaluate the application of a lambda abstraction to an argument expression. – A copy of the body of the lambda abstraction is ...
... • We can formally model the process of evaluating an expression as the application of one or more reduction rules. • E.g., lambda-calculus includes the beta-reduction rule to evaluate the application of a lambda abstraction to an argument expression. – A copy of the body of the lambda abstraction is ...
Effectively Polynomial Simulations
... m truth-preserving transformation from boolean formuWe next define automatizability. Like p-simulation las to boolean formulas if, for all boolean formulas f , f and effectively-p simulation, automatizability comes in is in TAUT (respectively QTAUT) if and only if R(f, m) two flavors: strong and wea ...
... m truth-preserving transformation from boolean formuWe next define automatizability. Like p-simulation las to boolean formulas if, for all boolean formulas f , f and effectively-p simulation, automatizability comes in is in TAUT (respectively QTAUT) if and only if R(f, m) two flavors: strong and wea ...
Curry: A Tutorial Introduction
... Curry is a universal programming language aiming at the amalgamation of the most important declarative programming paradigms, namely functional programming and logic programming. Curry combines in a seamless way features from functional programming (nested expressions, lazy evaluation, higher-order ...
... Curry is a universal programming language aiming at the amalgamation of the most important declarative programming paradigms, namely functional programming and logic programming. Curry combines in a seamless way features from functional programming (nested expressions, lazy evaluation, higher-order ...
full text (.pdf)
... e.g. Brandt and Henglein (1998); Hermida and Jacobs (1998); Milner and Tofte (1991); Niqui and Rutten (2009), not much has been explored when it comes to properties of other relations on coinductive datatypes besides equality. Our aim in this paper is to introduce an informal style of coinductive re ...
... e.g. Brandt and Henglein (1998); Hermida and Jacobs (1998); Milner and Tofte (1991); Niqui and Rutten (2009), not much has been explored when it comes to properties of other relations on coinductive datatypes besides equality. Our aim in this paper is to introduce an informal style of coinductive re ...
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.