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Questions tagged [predicate-logic]

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How to correctly negate a predicate bounded by some quantifiers?

this is a problem which was asked in GATE CS 2010. This is question statement: Q: Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. which ...
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In predicate logic, is the “environment” only needed when free variables are present?

Suppose there exist no free variables in a given predicate logic formula. Is then a model alone sufficient to fully interpret the formula and make inferences? Don't we need an environment or variable ...
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Predicate Logic - negating the conclusion to prove logical consequence?

In Predicate Logic, if you want to prove the logical consequence using the method of resolution, do you ALWAYS start off by negating the conclusion?
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Predicate Logics - double negation HELP me understand

Sorry for maybe a silly question but i need to understand how ¬(¬∀x ¬A(x)) equals ∀x ¬A(x) In my mind, the negation before the parenthesis will be applied to both ¬∀x and ¬A(x). So it would look like ...
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Computability: Proving a predicate is not recursively enumerable

Let P(p) <=> for each x, comp(p,x) is defined. Can anyone explain to me how to prove that P is not RE (recursively enumerable) ?
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Natural deduction proof without any predicate

I am gaving trouble proving a natural deduction proof when there is no predicate given. Only conclusion is given. I understand the rules of elimnations, inclusions, IPs and others but I having trouble ...
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1answer
68 views

Hoare triple: Loop invariant and correctness

The following Hoare triple in which variable a is an array of integers, and len, max, i, n, j and m are integer-valued variables. Provide a loop invariant (using predicate logic) suitable for proving ...
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0answers
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Hoare triple: Loop invariant and partial correctness

Below there is Hoare triple in which variable $a$ is an array of integers, $len$, $x, i$ are integer-valued variables, and $r$ is a Boolean-valued variable. I have to provide a loop invariant (using ...
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1answer
133 views

Negation of the semantics of the Until operator in LTL

I have been looking at the Until operator and the release operator and when introduced to the release operator it was suggested that it is equivalent to: $\phi R \psi \equiv \neg(\neg\phi U \neg \psi)...
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2answers
70 views

Must $x$ and $y$ be different in a statement of the form $\forall x \forall y \cdots$?

Given the following predicate formula $F$: $$\forall x \forall y [(\text{italian}(x) \Rightarrow (\text{winWC}(y) \Rightarrow \text{happy}(x))]$$ I am having trouble understanding whether $x$ and $y$...
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What does it mean to logically imply another predicate?

Consider the following predicate formulas. $F1: \forall x \exists y ( P(x) \to Q(y) ).$ $F2: \exists x \forall y ( P(x) \to Q(y) ).$ $F3: \forall x P(x) \to \exists y Q(y).$ $F4: \exists x P(x) \...
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1answer
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predicate logic proof of 2 numbers

For any two different numbers there is an number in between. I'm trying to write this in predicate logic and have no idea how to do it, since I need 2 variables X and Y? For all x there exists a y ...
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predicate logic/binary relation help

(1) ∀x, y, z (x < y ∧ y < z → x < z) (transitivity) (2) ∀x ¬(x < x) (antisymmetry) (3) ∀x, y (x < y ∨ x = y ∨ y < x) (linearity) I need to give an example of a (nonempty) ...
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1answer
62 views

Discrete Mathematics Proofs for ∃ and ∀

Premises or Givens: $∃x(A(x) → B(x))$ $∀x (B(x) → K(x))$ To Prove: $∃x(A(x) → K(x))$ My Solution: $A(z) → B(z)$ From premise and Existential instantiation $x$ for $z$ $B(z) → K(z)$ From ...