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Questions tagged [predicate-logic]

49 questions
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How do you differentiate between At least one X and Exactly one X in predicate logic?

Here are the following two sentences. At least one person speaks English. ∃E(x) Exactly one person speaks English. Instead of ∃E(x), what do I write?
Abercrombie Dorfen
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Is it possible to construct infinitely many non-equivalent formulas in predicate logic?

In the language of predicate logic with only identity and no predicates, function symbols, or constants, is it possible to construct infinitely many non-equivalent formulas?
Rajamani Sarvesh
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What are the advantages of Aristotle's term logic over predicate logic?

I have read Wikipedia's term logic entry, and the quote by Gareth Evans in the Revival section that's supposed to argue for term logic's advantages over predicate logic: "I come to semantic investigations with a preference for homophonic theories;…
MWB
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Proof Using Model Universe

Suppose I am trying to prove the following argument (∀x)(Cx → Dx), (∀x)(Ex → ~Dx), /∴ (∀x)(Ex → ~Cx) Now, let's also assume that I don't know if this argument is valid or not. Because of this, I try to check for invalidity using the model universe…
N. Bar
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ZFC Axioms and First Order Logic

I have never been formally trained in logic and philosophy. I became increasingly interested in the foundation of mathematics after I graduated from university. Recently, I've been self-studying ZFC set theory and have realized that mathematical…
Libertarian Feudalist Bot
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Are there paradoxes involved in allowing for an unrestricted domain in predicate logic?

I've put some thought into this, and just want to make sure I'm on track, or if I need to be corrected. Basically, my answer is this: Yes, you need to always specify a domain when formalizing into predicate logic, an unrestricted domain results in…
Kevin Holmes
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Why is first-order logic interesting to philosophers?

This site had a question: Is First Order Logic (FOL) the only fundamental logic? Let me ask the opposite: Why is FOL still interesting or useful to philosophers? For example, the "ancestor" relationship cannot even be defined in it. This alone shows…
MWB
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Is ¬(a = b) the same as (a ≠ b) in logic

Are these the same in predicate logic with identity: ¬ (a = b) a ≠ b I'm not quite sure whether they can be used interchangeably in proofs. Any help would be great!
CSWizard
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Philosophy book written using logic statements

I would like to translate a philosophy text into logic axioms and propositions. Then, I would like to use prolog to check if the text is logically consistent. However, I find it difficult to translate philosophy books into logic. Is there any…
Tereso del Río Almajano
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Understanding the syntax of subsitution

I have a question about the meaning and semantics of substitution, I apologise if this is off-topic but I thought here would be the best place as it's more about the semantics and meaning than any formal ideas or practical hindrances in Mathematics,…
Confused
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Could we supply logics make quantification over logical constants?

In first order logic, we make quantification over individuals, and in second order logic, we make quantification over properties. So could we supply logics make quantification over logical constants, e.g. over logical connectives, or modalities…
AnduinWilde
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Is al-Farabi right that predicates must add information and existence is not a predicate?

Al-Farabi claimed that existence is not a predicate, because "exists" as in "Apple is red and exists." doesn't bring any new information, but does a predicate have to bring in a new information in order to be a predicate? I thought a predicate only…
Sayaman
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Can 'All S is P' ever be false if S is empty?

I'm self-learning logic, I'm stuck on an issue similar to this question: In modern logic, why does "All S is P" contradict "Some S is not P"? In the boolean interpretation 'All S is P' doesn't imply existence of S, does that mean that it can never…
binarylegit
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What are some of the struggles that come with teaching formal logic?

I'm currently an undergraduate student who wants to do research on the pedagogy of formal logic. As a result, I wanted to know what are some challenges that instructors (or even students for that matter) encounter when teaching introductory formal…
TheSinisterEagle
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Is existential quantification in PL exclusive or modally inclusive of other existential quantifications in the same discourse universe?

In "(∃x, ∀x(Px)) ∧ (∃y, ∀y(Qy))", are the sets of x's and y's necessarily exclusive to each other, i.e. does the fact that we are using different variables (x and y) for them imply that NONE x can be a y? Or is the formula modally open to some x…
Nemo Nobody
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