CSE 452: Programming Languages
... Programs do not state exactly how a result is to be computed but rather describe the form of the result It is assumed that the computer can determine how the result is to be obtained One needs to provide the computer with the relevant information and a method of inference for computing desirable res ...
... Programs do not state exactly how a result is to be computed but rather describe the form of the result It is assumed that the computer can determine how the result is to be obtained One needs to provide the computer with the relevant information and a method of inference for computing desirable res ...
The Art of Ordinal Analysis
... proof, Gentzen used his sequent calculus and employed the technique of cut elimination. As this is a tool of utmost importance in proof theory and ordinal analysis, a rough outline of the underlying ideas will be discussed next. The most common logical calculi are Hilbert-style systems. They are spe ...
... proof, Gentzen used his sequent calculus and employed the technique of cut elimination. As this is a tool of utmost importance in proof theory and ordinal analysis, a rough outline of the underlying ideas will be discussed next. The most common logical calculi are Hilbert-style systems. They are spe ...
THE ABUNDANCE OF THE FUTURE A Paraconsistent Approach to
... “utility” of this logical approach in the worst case. In order to defeat criticisms of the second kind one should give a possible application, or at least a natural interpretation of this logic. Abundance has at least some intuitive grounding in our linguistic use: most of the times, when we say “ ...
... “utility” of this logical approach in the worst case. In order to defeat criticisms of the second kind one should give a possible application, or at least a natural interpretation of this logic. Abundance has at least some intuitive grounding in our linguistic use: most of the times, when we say “ ...
An introduction to digital electronics
... in a different way. The state of the switch does not change smoothly from off to on. It can’t be slightly on, and then a bit more on, and so on. It is on or off. The horizontal axis shows the time at which the change from on to off occurs. The output voltage always has one of two possible values. Th ...
... in a different way. The state of the switch does not change smoothly from off to on. It can’t be slightly on, and then a bit more on, and so on. It is on or off. The horizontal axis shows the time at which the change from on to off occurs. The output voltage always has one of two possible values. Th ...
logic for computer science - Institute for Computing and Information
... Gottlob Frege, a German mathematician working in relative obscurity. Frege aimed to derive all of mathematics from logical principles, in other words pure reason, together with some self-evident truths about sets. (Such as 'sets are identical if they have the same members' or 'every property determi ...
... Gottlob Frege, a German mathematician working in relative obscurity. Frege aimed to derive all of mathematics from logical principles, in other words pure reason, together with some self-evident truths about sets. (Such as 'sets are identical if they have the same members' or 'every property determi ...
Building explicit induction schemas for cyclic induction reasoning
... predicates [1]. We focuss on two representative systems, proposed by Brotherston [3,4]: i) the LKID structural system that integrates induction rules generalizing Noetherian induction reasoning by the means of schemas issued from the recursion analysis of (mutually defined) inductive predicates, and ...
... predicates [1]. We focuss on two representative systems, proposed by Brotherston [3,4]: i) the LKID structural system that integrates induction rules generalizing Noetherian induction reasoning by the means of schemas issued from the recursion analysis of (mutually defined) inductive predicates, and ...
Mathematical Logic. An Introduction
... Logical rules satisfy certain algebraic laws like associativity. Another interesting operation is substitution: From y = g(z) and z = f (x) infer y = g(f (x)) by a “find-and-replace”-substitution of z by f (x). Given a sufficient collection of rules, the above sequence of formulas, involving “keywor ...
... Logical rules satisfy certain algebraic laws like associativity. Another interesting operation is substitution: From y = g(z) and z = f (x) infer y = g(f (x)) by a “find-and-replace”-substitution of z by f (x). Given a sufficient collection of rules, the above sequence of formulas, involving “keywor ...
Lattice FPGA 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 ...
Modal Reasoning
... Bisimulations have two major uses; we consider tree unraveling first, then model contraction. Definition: Tree Unraveling Every modal M, s has a bisimulation with a rooted tree-like model constructed as follows. The worlds in the tree unraveling are all finite paths of worlds in M starting with s an ...
... Bisimulations have two major uses; we consider tree unraveling first, then model contraction. Definition: Tree Unraveling Every modal M, s has a bisimulation with a rooted tree-like model constructed as follows. The worlds in the tree unraveling are all finite paths of worlds in M starting with s an ...
The logic and mathematics of occasion sentences
... ABSTRACT. The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of ...
... ABSTRACT. The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of ...
relevant reasoning as the logical basis of
... extensional notion of material implication (denoted by → in this paper) which is defined as A→B =df ¬(A∧¬B) or A→B =df ¬A∨B. However, the material implication is just a truth-function of its antecedent and consequent but not requires that there must exist a necessarily relevant and/or conditional re ...
... extensional notion of material implication (denoted by → in this paper) which is defined as A→B =df ¬(A∧¬B) or A→B =df ¬A∨B. However, the material implication is just a truth-function of its antecedent and consequent but not requires that there must exist a necessarily relevant and/or conditional re ...
CERES for Propositional Proof Schemata
... This will yield our notion of proof schemata: I Definition 2.4 (Proof schemata). Let ψ be a proof symbol and S(n) be a sequent. Then a proof schema pair for ψ is a pair of LKS-proofs (π, ν(k + 1)) with end-sequents S(0) and S(k + 1) respectively such that π may not contain proof links and ν(k + 1) m ...
... This will yield our notion of proof schemata: I Definition 2.4 (Proof schemata). Let ψ be a proof symbol and S(n) be a sequent. Then a proof schema pair for ψ is a pair of LKS-proofs (π, ν(k + 1)) with end-sequents S(0) and S(k + 1) respectively such that π may not contain proof links and ν(k + 1) m ...
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.