Logic, Sets, and Proofs
... Often we are working with elements of a fixed set. In calculus, this fixed set is often the real numbers R or an interval [a, b] ⊆ R. In linear algebra, the fixed set is often Rn , Cn or an abstract vector space V (all of these terms will eventually be defined). In the discussion that follows, this ...
... Often we are working with elements of a fixed set. In calculus, this fixed set is often the real numbers R or an interval [a, b] ⊆ R. In linear algebra, the fixed set is often Rn , Cn or an abstract vector space V (all of these terms will eventually be defined). In the discussion that follows, this ...
CA320 - Computability & Complexity Overview
... truth value of x, is true for all values of x. ∃x(P(x))states that the proposition P, which depends on the truth value of x, is true for some value of x. Quantifiers can combined in the same expression but great care is needed. The following 2 expressions which are very similar mean 2 different thin ...
... truth value of x, is true for all values of x. ∃x(P(x))states that the proposition P, which depends on the truth value of x, is true for some value of x. Quantifiers can combined in the same expression but great care is needed. The following 2 expressions which are very similar mean 2 different thin ...
Verification and Specification of Concurrent Programs
... expressed in terms of these actions. To prove that one abstract program Π1 implements another abstract program Π2 , one must prove: 1. Every possible initial state of Π1 is a possible initial state of Π2 . 2. Every step allowed by Π1 ’s next-state relation is allowed by Π2 ’s next-state relation—a c ...
... expressed in terms of these actions. To prove that one abstract program Π1 implements another abstract program Π2 , one must prove: 1. Every possible initial state of Π1 is a possible initial state of Π2 . 2. Every step allowed by Π1 ’s next-state relation is allowed by Π2 ’s next-state relation—a c ...
PARADOX AND INTUITION
... 3. Paradoxes and mathematical intuition What does it really mean that some consequences of a given theorem are counterintuitive? Does it imply that there is something wrong with the axioms we have accepted? Or may be, there is something hidden in the arguments (rules of inference) applied in the pr ...
... 3. Paradoxes and mathematical intuition What does it really mean that some consequences of a given theorem are counterintuitive? Does it imply that there is something wrong with the axioms we have accepted? Or may be, there is something hidden in the arguments (rules of inference) applied in the pr ...
3x9: 9 E 9}, V{ A 8: 9 ES)
... by Theorem 16 in [4]) that Mx is the prime model of Tà . As said before, we take N = (J a
... by Theorem 16 in [4]) that Mx is the prime model of Tà . As said before, we take N = (J a
CSS conference sample
... [email protected] AbstractDifferent logic families have been proposed from several years to improve the performance of the high speed circuits. Mostly used logic family is CMOS which requires equal number of nMOS and pMOS transistor but in some application it may be required to reduce the area. Ps ...
... [email protected] AbstractDifferent logic families have been proposed from several years to improve the performance of the high speed circuits. Mostly used logic family is CMOS which requires equal number of nMOS and pMOS transistor but in some application it may be required to reduce the area. Ps ...
Modal Logic
... 4 Neighborhood Semantics: A remark on normal modal logics 20 5 Intuitionistic Propositional Calculus ...
... 4 Neighborhood Semantics: A remark on normal modal logics 20 5 Intuitionistic Propositional Calculus ...
Reasoning about Programs by exploiting the environment
... would then be incomplete for this new environment. Weakening the assumptions could add feasible behaviors; the logic for the original environment would then become unsound. For example, any of the programming logics for shared-memory concurrency (e.g. [0G76]) could be used to prove that program of F ...
... would then be incomplete for this new environment. Weakening the assumptions could add feasible behaviors; the logic for the original environment would then become unsound. For example, any of the programming logics for shared-memory concurrency (e.g. [0G76]) could be used to prove that program of F ...
1 The calculus of “predicates”
... We can introduce such predicates into a finite language. For example, if the base set is given by A 1,2,3,4 where 1,2,3,4 now really are numbers and no longer mere partitions of space, then each subset of A shall define a predicate: 2,4 is the predicate “... even number in A”. Two predicates s ...
... We can introduce such predicates into a finite language. For example, if the base set is given by A 1,2,3,4 where 1,2,3,4 now really are numbers and no longer mere partitions of space, then each subset of A shall define a predicate: 2,4 is the predicate “... even number in A”. Two predicates s ...
An Introduction to Löb`s Theorem in MIRI Research
... This expository note is devoted to answering the following question: why do many MIRI research papers cite a 1955 theorem of Martin Löb [12], and indeed, why does MIRI focus so heavily on mathematical logic? The short answer is that this theorem illustrates the basic kind of self-reference involved ...
... This expository note is devoted to answering the following question: why do many MIRI research papers cite a 1955 theorem of Martin Löb [12], and indeed, why does MIRI focus so heavily on mathematical logic? The short answer is that this theorem illustrates the basic kind of self-reference involved ...
Using linear logic to reason about sequent systems ?
... either lists, multisets, or sets of formulas. Sets are used if all three structural rules (exchange, weakening, contraction) are implicit; multisets are used if exchange is implicit; and lists are used if no structural rule is implicit. Since our goal here is to encode object-level sequents into met ...
... either lists, multisets, or sets of formulas. Sets are used if all three structural rules (exchange, weakening, contraction) are implicit; multisets are used if exchange is implicit; and lists are used if no structural rule is implicit. Since our goal here is to encode object-level sequents into met ...
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.