Semantics of intuitionistic propositional logic
... Example 2.13 Here are some examples of distributive lattices. The first, second and fourth lattices on the top row are boolean algebras, while the other lattices are not. (Exercise: in each such case find the elements which lack complements.) ...
... Example 2.13 Here are some examples of distributive lattices. The first, second and fourth lattices on the top row are boolean algebras, while the other lattices are not. (Exercise: in each such case find the elements which lack complements.) ...
Set Theory II
... Last time we discussed the Axioms of Extension, Specification, Unordered Pairs, and Unions. Some more aioms of set theory Powers For each set there exists a collection of sets that contains among its elements all the subsets of the given set. (Combined with the Axiom of Specification, it follows tha ...
... Last time we discussed the Axioms of Extension, Specification, Unordered Pairs, and Unions. Some more aioms of set theory Powers For each set there exists a collection of sets that contains among its elements all the subsets of the given set. (Combined with the Axiom of Specification, it follows tha ...
MoggiMonads.pdf
... This paper is about logics for reasoning about programs, in particular for proving equivalence of programs. Following a consolidated tradition in theoretical computer science we identify programs with the closed λ-terms, possibly containing extra constants, corresponding to some features of the prog ...
... This paper is about logics for reasoning about programs, in particular for proving equivalence of programs. Following a consolidated tradition in theoretical computer science we identify programs with the closed λ-terms, possibly containing extra constants, corresponding to some features of the prog ...
Array Logics and VLSI Design
... Based upon ability to represent combinational logic Sum of products form Build circuits as combinations of min terms These are typically two level AND-OR devices Can realize any sum of products expression Only restriction is size of device Number of input pins Number of output pins Number of product ...
... Based upon ability to represent combinational logic Sum of products form Build circuits as combinations of min terms These are typically two level AND-OR devices Can realize any sum of products expression Only restriction is size of device Number of input pins Number of output pins Number of product ...
Propositional and predicate logic - Computing Science
... Argument 1: If the program syntax is faulty or if program execution results in division by zero, then the computer will generate an error message. Therefore, if the computer does not generate an error message, then the program syntax is correct and program execution does not result in division by ze ...
... Argument 1: If the program syntax is faulty or if program execution results in division by zero, then the computer will generate an error message. Therefore, if the computer does not generate an error message, then the program syntax is correct and program execution does not result in division by ze ...
Programming Language Semantics with Isabelle/HOL
... Proof assistants are computer systems that allow a user to do mathematics on a computer, where the proving and defining of mathematics is emphasized, rather than the computational (numeric or symbolic) aspect of it [3]. Thus a user can set up a mathematical theory, define properties and do logical r ...
... Proof assistants are computer systems that allow a user to do mathematics on a computer, where the proving and defining of mathematics is emphasized, rather than the computational (numeric or symbolic) aspect of it [3]. Thus a user can set up a mathematical theory, define properties and do logical r ...
Propositional logic - Computing Science
... should be acceptable on their own merits or follow from other statements that are known to be true. [Q] Any logical forms for valid arguments? Examples ...
... should be acceptable on their own merits or follow from other statements that are known to be true. [Q] Any logical forms for valid arguments? Examples ...
paper by David Pierce
... C, and they use Peano’s sign ∈ for membership of an individual in a class (originally the sign is an epsilon, for the Greek âst ‘is’ [26, pp. 25–26]). Dedekind himself does not distinguish between this membership relation and the subset relation: he used the same sign for both, looking something li ...
... C, and they use Peano’s sign ∈ for membership of an individual in a class (originally the sign is an epsilon, for the Greek âst ‘is’ [26, pp. 25–26]). Dedekind himself does not distinguish between this membership relation and the subset relation: he used the same sign for both, looking something li ...
A Proof Theory for Generic Judgments
... The operational semantics of a computation system is often presented as inference rules or, equivalently, as logical theories. Specifications can be made more declarative and high-level if syntactic details concerning bound variables and substitutions are encoded directly into the logic using term-l ...
... The operational semantics of a computation system is often presented as inference rules or, equivalently, as logical theories. Specifications can be made more declarative and high-level if syntactic details concerning bound variables and substitutions are encoded directly into the logic using term-l ...
Proof translation for CVC3
... Tautologies (not always) Extra clauses asserted by theory solvers ...
... Tautologies (not always) Extra clauses asserted by theory solvers ...
Lecture 4 - Michael De
... Assume that instead of interpreting i as a gap, we interpret it as a glut. But then taking the value i means being both true and false, and hence true, and hence designated. So we need to add i to D. The resulting logic is called LP, or the Logic of Paradox, as Priest originally called it. It is the ...
... Assume that instead of interpreting i as a gap, we interpret it as a glut. But then taking the value i means being both true and false, and hence true, and hence designated. So we need to add i to D. The resulting logic is called LP, or the Logic of Paradox, as Priest originally called it. It is the ...
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.