Propositional Logic First Order Logic
... Satisfiability and validity Normal forms Deductive proofs and resolution Modeling with Propositional logic ...
... Satisfiability and validity Normal forms Deductive proofs and resolution Modeling with Propositional logic ...
Redundancies in the Hilbert-Bernays derivability conditions for
... hypothesis (2), which is of course a form of the third derivability condition of Hilbert and Bernays [3] , gives a "best possiblerr result in terms of the general class of logics treated in Theorem 1. To see this is the case, one need only consider Kreisel's example of a logic P* on page 154 of [6]. ...
... hypothesis (2), which is of course a form of the third derivability condition of Hilbert and Bernays [3] , gives a "best possiblerr result in terms of the general class of logics treated in Theorem 1. To see this is the case, one need only consider Kreisel's example of a logic P* on page 154 of [6]. ...
PPT
... Now suppose Q were not provable. Then, P(G(Q)) would not be provable, because a proof definitely doesn’t exist. But Q is false iff G(Q) is provable. This is a contradiction. But wait! If Q isn’t provable (which we just showed), then it’s true! ...
... Now suppose Q were not provable. Then, P(G(Q)) would not be provable, because a proof definitely doesn’t exist. But Q is false iff G(Q) is provable. This is a contradiction. But wait! If Q isn’t provable (which we just showed), then it’s true! ...
Sample Exam 1 - Moodle
... CSC 4-151 Discrete Mathematics for Computer Science Exam 1 May 7, 2017 ____________________ name For credit on these problems, you must show your work. On this exam, take the natural numbers to be N = {0,1,2,3, …}. 1. (6 pts.) State and prove one of DeMorgan’s Laws for propositional logic, using a t ...
... CSC 4-151 Discrete Mathematics for Computer Science Exam 1 May 7, 2017 ____________________ name For credit on these problems, you must show your work. On this exam, take the natural numbers to be N = {0,1,2,3, …}. 1. (6 pts.) State and prove one of DeMorgan’s Laws for propositional logic, using a t ...
Lesson 1
... This apple is an agaric. ---------------------------------------------------------------------Hence This apple has a strong toxic effect. The argument is valid. But the conclusion is evidently not true (false). Hence, at least one premise is false (obviously the second). Circumstances according to ...
... This apple is an agaric. ---------------------------------------------------------------------Hence This apple has a strong toxic effect. The argument is valid. But the conclusion is evidently not true (false). Hence, at least one premise is false (obviously the second). Circumstances according to ...
Logic - Decision Procedures
... (4) None of them, that are written on one sheet, are undated; (5) All of them, that are not crossed, are in black ink; (6) All of them, written by Brown, begin with "Dear Sir"; (7) All of them, written on blue paper, are filed; (8) None of them, written on more than one sheet, are crossed; (9) None ...
... (4) None of them, that are written on one sheet, are undated; (5) All of them, that are not crossed, are in black ink; (6) All of them, written by Brown, begin with "Dear Sir"; (7) All of them, written on blue paper, are filed; (8) None of them, written on more than one sheet, are crossed; (9) None ...
Curry`s paradox, Lukasiewicz, and Field
... Indeterminate, neither-true-nor-false. And we’ll write |ϕ| for the value of ϕ. Then, rather neatly, we have in the three-valued case that, for all ϕ, ψ, 1. |¬ϕ| = 1 − |ϕ| 2. |ϕ ∧ ψ| = min(|ϕ|, |ψ|) 3. |ϕ ∨ ψ| = max(|ϕ|, |ψ|) 4. |ϕ → ψ| = min(1, 1 − |ϕ| + |ψ|) These, of course, aren’t the only equat ...
... Indeterminate, neither-true-nor-false. And we’ll write |ϕ| for the value of ϕ. Then, rather neatly, we have in the three-valued case that, for all ϕ, ψ, 1. |¬ϕ| = 1 − |ϕ| 2. |ϕ ∧ ψ| = min(|ϕ|, |ψ|) 3. |ϕ ∨ ψ| = max(|ϕ|, |ψ|) 4. |ϕ → ψ| = min(1, 1 − |ϕ| + |ψ|) These, of course, aren’t the only equat ...
A(x)
... Formula A is true in interpretation I, |=I A, if for all possible valuations v holds that |=I A[v]. Model of formula A is interpretation I, in which is A true (that means for all valuations of free variables). Formula A is satisfiable, if there is interpretation I, in which A is satisfied (i.e., if ...
... Formula A is true in interpretation I, |=I A, if for all possible valuations v holds that |=I A[v]. Model of formula A is interpretation I, in which is A true (that means for all valuations of free variables). Formula A is satisfiable, if there is interpretation I, in which A is satisfied (i.e., if ...
Propositional and Predicate Logic - IX
... Suppose for a contradiction that ϕ is not valid in T , i.e. there exists a model A of the theory T in which ϕ is not true (a counterexample). Since A agrees with the root entry F ϕ, by the previous lemma, A can be expanded to the language LC so that it agrees with some branch in τ . But this is impo ...
... Suppose for a contradiction that ϕ is not valid in T , i.e. there exists a model A of the theory T in which ϕ is not true (a counterexample). Since A agrees with the root entry F ϕ, by the previous lemma, A can be expanded to the language LC so that it agrees with some branch in τ . But this is impo ...
REVERSE MATHEMATICS Contents 1. Introduction 1 2. Second
... often used. Z2 is a formal system consisting of language L2 and some axioms. From these axioms, we can deduce formulas, called theorems of Z2 . A subsystem of second-order arithmetic is a formal system consisting of language L2 and axioms that are theorems of Z2 ; a subsystem consists of some of the ...
... often used. Z2 is a formal system consisting of language L2 and some axioms. From these axioms, we can deduce formulas, called theorems of Z2 . A subsystem of second-order arithmetic is a formal system consisting of language L2 and axioms that are theorems of Z2 ; a subsystem consists of some of the ...
Curry`s Paradox. An Argument for Trivialism
... 2006a, 2006), Priest claims that dialetheism supplies the best solution to the the strengthen liar paradox, a paradox originated from the sentence: (a): (a) is not true by holding that (a) is both true and not true. More generally, he holds that the paradoxical sentences obtained from self-reference ...
... 2006a, 2006), Priest claims that dialetheism supplies the best solution to the the strengthen liar paradox, a paradox originated from the sentence: (a): (a) is not true by holding that (a) is both true and not true. More generally, he holds that the paradoxical sentences obtained from self-reference ...
Russell`s logicism
... talking about the number 3, and number in general, as properties or characteristics. Now he is moving from this to talking about the number 3, and number in general, as sets. The next question is, what sets are they? Russell says: “Reurning now to the definition of number, it is clear that number i ...
... talking about the number 3, and number in general, as properties or characteristics. Now he is moving from this to talking about the number 3, and number in general, as sets. The next question is, what sets are they? Russell says: “Reurning now to the definition of number, it is clear that number i ...
Constructive Mathematics in Theory and Programming Practice
... excellent reference for the work of the Markov School is Kushner [1985]. By the mid-1960s it appeared that constructive mathematics was at best a minor activity, with few positive developments to show in comparison with the prodigious advances in traditional mathematics throughout the century. Indee ...
... excellent reference for the work of the Markov School is Kushner [1985]. By the mid-1960s it appeared that constructive mathematics was at best a minor activity, with few positive developments to show in comparison with the prodigious advances in traditional mathematics throughout the century. Indee ...
Definability properties and the congruence closure
... Sxyq~(x, y)<,~o(x, y) defines a Souslin tree, Gxyzq)(x, y, z)<:~o(x, y, z) defines the operation of a finitely generated group, R~,Xl,..., x,q)(xl,..., x,)<*there is a set of x indiscernibles for ~0 in the field of ~o, and we show, via a uniform counterexample, that both properties fail for any regu ...
... Sxyq~(x, y)<,~o(x, y) defines a Souslin tree, Gxyzq)(x, y, z)<:~o(x, y, z) defines the operation of a finitely generated group, R~,Xl,..., x,q)(xl,..., x,)<*there is a set of x indiscernibles for ~0 in the field of ~o, and we show, via a uniform counterexample, that both properties fail for any regu ...
study guide.
... Caesar cipher: if letters of the alphabet are numbered from 0to25, then a letter i is encoded by the letter j with the number j ≡ i + 3 mod 26. Here, instead of 3 one can take any other number. To decode, take i = j − 3 mod 26. In private-key cryptography, the code is obtained by doing a XOR of the ...
... Caesar cipher: if letters of the alphabet are numbered from 0to25, then a letter i is encoded by the letter j with the number j ≡ i + 3 mod 26. Here, instead of 3 one can take any other number. To decode, take i = j − 3 mod 26. In private-key cryptography, the code is obtained by doing a XOR of the ...
