First-Order Theorem Proving and Vampire

... http://www.tptp.org contains a large collection of first-order problems. For representing these problems it uses the TPTP syntax, which is understood by all modern theorem provers, including Vampire. In the TPTP syntax this group theory problem can be written down as follows: %---- 1 * x = 1 fof(lef ...

... http://www.tptp.org contains a large collection of first-order problems. For representing these problems it uses the TPTP syntax, which is understood by all modern theorem provers, including Vampire. In the TPTP syntax this group theory problem can be written down as follows: %---- 1 * x = 1 fof(lef ...

a-logic - Digital Commons@Wayne State University

... Whitehead’s great book, Principia Mathematica (1913) of Quine’s Mathematical Logic (1940) and Methods of Logic (4th ed.,1982) and of hundreds of other textbooks and treatises which have the same set of theorems, the same semantical foundations, and use the same concepts of validity and logical truth ...

... Whitehead’s great book, Principia Mathematica (1913) of Quine’s Mathematical Logic (1940) and Methods of Logic (4th ed.,1982) and of hundreds of other textbooks and treatises which have the same set of theorems, the same semantical foundations, and use the same concepts of validity and logical truth ...

code-carrying theory - Computer Science at RPI

... reachable, his door was always open. We held hundreds of meetings, sometimes discussing for hours either in his office or through email. There were times that he even worked harder on this project than I did. He is a good friend, a thoughtful person, and a real problem solver. I will always miss his ...

... reachable, his door was always open. We held hundreds of meetings, sometimes discussing for hours either in his office or through email. There were times that he even worked harder on this project than I did. He is a good friend, a thoughtful person, and a real problem solver. I will always miss his ...

2102-282 Digital Electronics - IC Design & Application Research Lab.

... Hold time, thold is the time that the data inputs must remain valid after the clock edge ...

... Hold time, thold is the time that the data inputs must remain valid after the clock edge ...

Incompleteness

... Definition 1.7. Let A, B be two structures for a first-order language L “ tRi , fi , ci u. A homomorphism π from A to B is a map π : A Ñ B satisfying: RA pa1 , . . . an q iff RB pπpa1 q, . . . πpan qq, πpf A pa1 , . . . , an qq “ f B pπpa1 q, . . . , πpan qq, and πpcA q “ cB for all a1 , . . . , an ...

... Definition 1.7. Let A, B be two structures for a first-order language L “ tRi , fi , ci u. A homomorphism π from A to B is a map π : A Ñ B satisfying: RA pa1 , . . . an q iff RB pπpa1 q, . . . πpan qq, πpf A pa1 , . . . , an qq “ f B pπpa1 q, . . . , πpan qq, and πpcA q “ cB for all a1 , . . . , an ...

JUXTAPOSITION - Brown University

... of propositional logics. The approach to semantics employed here is broadly algebraic. I consider two semantic frameworks. The first involves sets of logical matrices, algebras with an arbitrary set of designated values. The second, more interesting, framework involves sets of unital matrices, algeb ...

... of propositional logics. The approach to semantics employed here is broadly algebraic. I consider two semantic frameworks. The first involves sets of logical matrices, algebras with an arbitrary set of designated values. The second, more interesting, framework involves sets of unital matrices, algeb ...

Simply Logical: Intelligent Reasoning by Example

... presentation starts with propositional clausal logic, and proceeds via relational clausal logic (without functors) to full clausal logic, and finally arrives at definite clause logic. Since the semantics of clausal logic is defined in its own terms, without reference to the kind of models employed i ...

... presentation starts with propositional clausal logic, and proceeds via relational clausal logic (without functors) to full clausal logic, and finally arrives at definite clause logic. Since the semantics of clausal logic is defined in its own terms, without reference to the kind of models employed i ...

Independence logic and tuple existence atoms

... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...

... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...

Artificial Intelligence

... • In fuzzy rules, the linguistic variable speed also has the range (the universe of discourse) between 0 and 220 km/h, but this range includes fuzzy sets, such as slow, medium and fast. The universe of discourse of the linguistic variable stopping_distance can be between 0 and 300 m and may include ...

... • In fuzzy rules, the linguistic variable speed also has the range (the universe of discourse) between 0 and 220 km/h, but this range includes fuzzy sets, such as slow, medium and fast. The universe of discourse of the linguistic variable stopping_distance can be between 0 and 300 m and may include ...

Standard ML: A Quick Tutorial

... accomplished by carrying the state around explicitly rather than implicitly Looping is accomplished via recursion rather than sequencing ...

... accomplished by carrying the state around explicitly rather than implicitly Looping is accomplished via recursion rather than sequencing ...

funprog

... E1, E2,...,En - E1 should evaluate to a function and then apply the function value of E1 to the arguments given by the values of E2,...,En. In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various special forms such as quote and if must be handled sep ...

... E1, E2,...,En - E1 should evaluate to a function and then apply the function value of E1 to the arguments given by the values of E2,...,En. In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various special forms such as quote and if must be handled sep ...

Introduction to Computational Logic

... and interactive theorem proving with the proof assistant Coq. At Saarland University the course is taught in this format since 2010. Students are expected to be familiar with basic functional programming and the structure of mathematical definitions and proofs. Talented students at Saarland Universi ...

... and interactive theorem proving with the proof assistant Coq. At Saarland University the course is taught in this format since 2010. Students are expected to be familiar with basic functional programming and the structure of mathematical definitions and proofs. Talented students at Saarland Universi ...

# 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.