Questions tagged [predicate-logic]

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Proving a predicate assignment is correct

I am currently reading Formal Methods - An Appetizer and am stuck in chapter 3 (Program Verification). I am unfamiliar with logic and I do not think I understand the $\vDash$ notation correctly. I ...
1 vote
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Prove that any first-order logics with equality and a relation/functional symbol of arity more than 1 is undecidable

Definition: A formal logic system is decidable – if there is an algorithm that can determine if any given sentence is a theorem (or not). Based on this definition, I am not sure how to move to prove ...
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Why is “For all the simple things you have done to me, there exists one thing that makes me happy” FALSE? Use nested quantifiers to prove your point

I've done my due dilligence and tried to answer this question using every resource I could get. KhanAcademy, NesoAcademy, and Rosen's Discrete Mathematics book. I still can't wrap my head around it. ...
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Complexity of pattern matching for modus ponens logical conclusions

Is a Turing machine with added the following contant-time operation equivalent (in the sense that polynomial time remains polynomial time and exponential time remains exponential time) to a (usual) ...
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1 vote
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Prolog: Deletion of all appearances of an element in a list

I am trying to create a predicate in Prolog which allows me to delete all occurrences of X in a list L. I have the following code: ...
193 views

Encoding the theorem on friends and strangers in predicate logic

In every group chat of six (distinct) people on Instagram, there is a group of three (distinct) people such that either: everyone in the group are friends everyone in the group are strangers (i.e not ...
218 views

Show that exist a finite set of clauses F in first-order logic that Res*(F) is infinite

I'm kind of desperate at this point about this question. A predicate-logic resolution derivation of a clause $C$ from a set of clauses $F$ is a sequence of clauses $C_1,\dots,C_m$, with $C_m = C$ ...
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184 views

Combining Predicate Logic and BigO

I am a beginner to predicate logic and BigO and am having though time understanding the definition of BigO in terms of predicate logic in the picture attached. I particularly am unable to understand ...
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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?
1 vote
26 views

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 ...
126 views

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) ?
1 vote
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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 ...
241 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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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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1 vote
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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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1 vote
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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 ...
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