Logic gate
... outputs in order to determine the "true" logic function indicated. All logic relations can be realized by using NAND gates (this can also be done using NOR gates). De Morgan's theorem is most commonly used to transform all logic gates to NAND gates or NOR gates. This is done mainly since it is easy ...
... outputs in order to determine the "true" logic function indicated. All logic relations can be realized by using NAND gates (this can also be done using NOR gates). De Morgan's theorem is most commonly used to transform all logic gates to NAND gates or NOR gates. This is done mainly since it is easy ...
CSE 20 - Lecture 14: Logic and Proof Techniques
... Negating a sentence: iclicker What is the negation of the sentence: “There is an university in USA where every department has at least 20 faculty and at least one noble laureate.” There is an university in USA where every department has less than 20 faculty and at least one noble laureate. All univ ...
... Negating a sentence: iclicker What is the negation of the sentence: “There is an university in USA where every department has at least 20 faculty and at least one noble laureate.” There is an university in USA where every department has less than 20 faculty and at least one noble laureate. All univ ...
The Pure Calculus of Entailment Author(s): Alan Ross Anderson and
... constructing proofs (though of course the distinction is heuristic rather than logical), and we therefore call this the Test Formulation of Fitch's system. In order to motivate the Test Formulation, we notice that with each i-th step Ai in the proofs above there is associated first a number of verti ...
... constructing proofs (though of course the distinction is heuristic rather than logical), and we therefore call this the Test Formulation of Fitch's system. In order to motivate the Test Formulation, we notice that with each i-th step Ai in the proofs above there is associated first a number of verti ...
First Order Predicate Logic
... A path in a tableaux is contradictory or closed if some atomic formulae α and ~ α appear on the same path. If all the paths of a tableau are closed, then it is called a contradictory tableaux. A tableau proof of a formula α is a contradictory tableau with root as ~ α . Let α be any formula. If table ...
... A path in a tableaux is contradictory or closed if some atomic formulae α and ~ α appear on the same path. If all the paths of a tableau are closed, then it is called a contradictory tableaux. A tableau proof of a formula α is a contradictory tableau with root as ~ α . Let α be any formula. If table ...
Note 2 - inst.eecs.berkeley.edu
... More specifically, a proof is typically structured as follows. Recall that there are certain statements, called axioms or postulates, that we accept without proof (we have to start somewhere). Starting from these axioms, a proof consists of a sequence of logical deductions: Simple steps that apply t ...
... More specifically, a proof is typically structured as follows. Recall that there are certain statements, called axioms or postulates, that we accept without proof (we have to start somewhere). Starting from these axioms, a proof consists of a sequence of logical deductions: Simple steps that apply t ...
Propositional Logic What is logic? Propositions Negation
... • Essentially, logic formalizes our reasoning process. – It provides a common language through which we can demonstrate to each other that our reasoning is valid. ...
... • Essentially, logic formalizes our reasoning process. – It provides a common language through which we can demonstrate to each other that our reasoning is valid. ...
L12_Slides
... programming these devices. Due to the large number of programmable switches in commercial chips; it is not feasible to specify manually the desired programming state for each switch. CAD systems are used to solve this problem. Computer system that runs the CAD tools is connected to a programming uni ...
... programming these devices. Due to the large number of programmable switches in commercial chips; it is not feasible to specify manually the desired programming state for each switch. CAD systems are used to solve this problem. Computer system that runs the CAD tools is connected to a programming uni ...
Note 2 - EECS: www-inst.eecs.berkeley.edu
... More specifically, a proof is typically structured as follows. Recall that there are certain statements, called axioms or postulates, that we accept without proof (we have to start somewhere). Starting from these axioms, a proof consists of a sequence of logical deductions: Simple steps that apply t ...
... More specifically, a proof is typically structured as follows. Recall that there are certain statements, called axioms or postulates, that we accept without proof (we have to start somewhere). Starting from these axioms, a proof consists of a sequence of logical deductions: Simple steps that apply t ...
Proofs
... thus the procedure does not halt. If ABSURD does not halt then we will exit the program and halt. Hence, ABSURD halts if it doesn't and doesn't halt if it does which is an obvious contradiction. Hence such a program does not exist. Q. E. D. Proofs ...
... thus the procedure does not halt. If ABSURD does not halt then we will exit the program and halt. Hence, ABSURD halts if it doesn't and doesn't halt if it does which is an obvious contradiction. Hence such a program does not exist. Q. E. D. Proofs ...
The Expressive Power of Modal Dependence Logic
... atoms, =(p1 , . . . , pn , q). The intuitive meaning of the formula =(p1 , . . . , pn , q) is that within a team the truth value of the proposition q is functionally determined by the truth values of the propositions p1 , . . . , pn . Modal dependence logic is a first step toward combining functiona ...
... atoms, =(p1 , . . . , pn , q). The intuitive meaning of the formula =(p1 , . . . , pn , q) is that within a team the truth value of the proposition q is functionally determined by the truth values of the propositions p1 , . . . , pn . Modal dependence logic is a first step toward combining functiona ...
Hybrid Interactive Theorem Proving using Nuprl and HOL?
... is based on a casting of Tait's computability argument in terms of semantics of a type system. This idea has been used to give an elegant proof of strong normalization of system F [11]. Nuprl can extract a \program" from our classical proof, but it will contain a term that represents an uncomputable ...
... is based on a casting of Tait's computability argument in terms of semantics of a type system. This idea has been used to give an elegant proof of strong normalization of system F [11]. Nuprl can extract a \program" from our classical proof, but it will contain a term that represents an uncomputable ...
The Logic of Atomic Sentences
... since b = d, c is left of d by the Indiscernibility of Identicals. But we are also told that d is left of e, and consequently c is to the left of e, by the textbftransitivity of left of. Done. William Starr — The Logic of Atomic Sentences (Phil 201.02) — Rutgers University ...
... since b = d, c is left of d by the Indiscernibility of Identicals. But we are also told that d is left of e, and consequently c is to the left of e, by the textbftransitivity of left of. Done. William Starr — The Logic of Atomic Sentences (Phil 201.02) — Rutgers University ...
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.