Logic Design
... variable by ‘0’ and ‘1’ Logic circuits are usually implemented using logic gates Circuits in which the output is determined solely by the current inputs are termed combinational logic circuits Logic functions can be described by truth tables or using ...
... variable by ‘0’ and ‘1’ Logic circuits are usually implemented using logic gates Circuits in which the output is determined solely by the current inputs are termed combinational logic circuits Logic functions can be described by truth tables or using ...
Document
... • Consider the logic block that has an output E that is true only if exactly two of the three inputs A, B, C are true Multiple correct equations: Two must be true, but all three cannot be true: E = ((A . B) + (B . C) + (A . C)) . (A . B . C) ...
... • Consider the logic block that has an output E that is true only if exactly two of the three inputs A, B, C are true Multiple correct equations: Two must be true, but all three cannot be true: E = ((A . B) + (B . C) + (A . C)) . (A . B . C) ...
Classical BI - UCL Computer Science
... Accordingly, the contexts Γ on the left-hand side of the sequents in the rules above are not sets or sequences, as in standard sequent calculi, but rather bunches: trees whose leaves are formulas and whose internal nodes are either ‘;’ or ‘,’ denoting respectively additive and multiplicative combina ...
... Accordingly, the contexts Γ on the left-hand side of the sequents in the rules above are not sets or sequences, as in standard sequent calculi, but rather bunches: trees whose leaves are formulas and whose internal nodes are either ‘;’ or ‘,’ denoting respectively additive and multiplicative combina ...
Aristotle`s particularisation
... He showed that the axiomatisation Lε of classical Aristotlean predicate logic proposed by him as a first order ε-predicate calculus—in which he used a primitive choice-function symbol, ‘ε’, for defining the quantifiers ‘∀’ and ‘∃’—would adequately express, and yield under a sound interpretation, Ari ...
... He showed that the axiomatisation Lε of classical Aristotlean predicate logic proposed by him as a first order ε-predicate calculus—in which he used a primitive choice-function symbol, ‘ε’, for defining the quantifiers ‘∀’ and ‘∃’—would adequately express, and yield under a sound interpretation, Ari ...
Failures of Categoricity and Compositionality for
... and sets thereof which are categorical in the sense of uniquely extending an assignment of semantic values to the atomic sentences of a language. Garson’s results are most impressive when we restrict ourselves to the intuitionistic propositional calculus. He shows that when we generalize our semant ...
... and sets thereof which are categorical in the sense of uniquely extending an assignment of semantic values to the atomic sentences of a language. Garson’s results are most impressive when we restrict ourselves to the intuitionistic propositional calculus. He shows that when we generalize our semant ...
A + B + C
... In POS standard form, every variable in the domain must appear in each sum term of the expression. You can expand a nonstandard POS expression to standard form by adding the product of the missing variable and its complement and applying rule 12, which states that (A + B)(A + C) = A + BC. Convert X ...
... In POS standard form, every variable in the domain must appear in each sum term of the expression. You can expand a nonstandard POS expression to standard form by adding the product of the missing variable and its complement and applying rule 12, which states that (A + B)(A + C) = A + BC. Convert X ...
Logic: Introduction - Department of information engineering and
... Modern Logic teaches us that one claim is a logical consequence of another if there is no way the latter could be true without the former also being true. It is also used to disconfirm a theory if a particular claim is a logical consequence of a theory, and we discover that the claim is false, then ...
... Modern Logic teaches us that one claim is a logical consequence of another if there is no way the latter could be true without the former also being true. It is also used to disconfirm a theory if a particular claim is a logical consequence of a theory, and we discover that the claim is false, then ...
Lecture Slides
... An international committee of researchers initiates the development of Haskell, a standard lazy functional language. Partially in response to “Can programming be liberated from the Von Neuman style?”, by John Backus. (Named in honor of logician Haskell B. Curry.) ...
... An international committee of researchers initiates the development of Haskell, a standard lazy functional language. Partially in response to “Can programming be liberated from the Von Neuman style?”, by John Backus. (Named in honor of logician Haskell B. Curry.) ...
Adding the Everywhere Operator to Propositional Logic (pdf file)
... denotes the infinite set of inference rules constructed by replacing metavariables α and β by formulas. (Similarly for the axiom schemes.) In PM (as in all the logics in this paper), a theorem is either an axiom or the conclusion of an inference rule whose premises are theorems. We use the notation ...
... denotes the infinite set of inference rules constructed by replacing metavariables α and β by formulas. (Similarly for the axiom schemes.) In PM (as in all the logics in this paper), a theorem is either an axiom or the conclusion of an inference rule whose premises are theorems. We use the notation ...
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.