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Questions tagged [modal-logic]

a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality

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Can modal logic be used to define the notion of an “arbitrary constant” in FOL?

I was wondering if first-order logic can be reduced to propositional calculus if we eliminate quantification. For example, instead of saying “for all x in a domain D, P(x)”, we could state “P(x)” for ...
lee pappas's user avatar
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Can the Good Samaritan problem of deontic logic be resolved by reinterpreting the deontic obligatory operator as the modal necessity operator?

The Good Samaritan problem of deontic logic It seems true that the starving ought to be fed. Now if the starving are fed then there are starving people. By a standard axiom of normal deontic logic ⊢ ...
lee pappas's user avatar
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What is the reason behind the fourth axiom in Gödel's ontological proof?

In Gödel's ontological proof, axiom 4 goes like this: And I'm not sure about what it means. If that P(φ) is true, then isn't it necessarily true as well? There's some basic concept about modal logic ...
Elvis's user avatar
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Do universals exist in all possible worlds?

Exactly what it says on the tin: Do abstract objects, like universals for instance, necessarily exist in all possible worlds? To my knowledge, David Lewis held to the opinion that they did (And that ...
Johnathan Green's user avatar
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Is B(p) V B(~p) an instance of LEM in doxastic logic?

So in classical logic either p is T or p is F. But is it same in doxastic logic, ie, is B(p) V B(~p) an instance of LEM? And the second issue, is it equivalent to B(p) V ~B(p)?
Vihan 's user avatar
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Understanding possible world semantics and time

In possible world semantics, statements of the form "It is possible that P" are interpreted as meaning "There is some 'possible world' in which P is true". And if you're a modal ...
Benjamin Grange's user avatar
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3 answers
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Can you help me understand the masked man paradox?

The masked man fallacy (or paradox) is roughly: Premise 1: I don't know who the man wearing the mask is. Premise 2: The man wearing the mask is my father. Premise 3: I know who my father is. ...
Benjamin Grange's user avatar
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When is the proposition expressed by "I am here" necessary?

I'm currently reading Kaplan's On The Logic of Demonstratives (1979). He considers the example (1) I am here now. and on page 84 he argues that (b) In almost (if not all) contexts, an utterance of (...
Harpagos's user avatar
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Proof that the single variable fragment of first order logic is equivalent to an S5-like modal logic

I think I read that a single sorted logic is a logic in which there is only one unique variable symbol permitted. In other words, there is only one “parameter of variation” amongst all sentences of ...
Julius Hamilton's user avatar
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Can there be nested possible worlds semantics?

Fairly straightforward question, I'd think: Usually, when we do Modal Logic, we think of propositions as sort of embedded within a framework of possible worlds. What, then, do we make of propositions ...
Johnathan Green's user avatar
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What is the modality of a statement that follows from a necessary statement?

Let □P. Suppose □P => Q. What can be said about the modality of Q? □P <=> P holds in every possible world. Thus it is available as a premise to derive Q in every possible world. Suppose Q is ...
Wowser's user avatar
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Questioning the category of the “moral”

Briefly: it occurs to me that taking as given the pre-existence of the terms “morality” and “ethics” structures our thinking preemptively and heavily. In the manner of discursive analysts like ...
Julius Hamilton's user avatar
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1 answer
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Do the incompleteness theorems need the provability predicate to be expressed, or can they be expressed via just ⊢?

In his "Epistemic Set Theory," William Reinhardt says: It is the purpose of this paper to formulate axioms for Gödel's modal operator B for provability (see [3], [8]) in the context of set ...
Kristian Berry's user avatar
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Modal dualism: is there a combination of counterpart and transworld-identity theory classifying objects based on which relation they enter into?

Theorists love to be competitive, but often enough we find out that they don't have to be like that. The SEP article on infinitesimals, for example, notes at one point: It is of interest to note that ...
Kristian Berry's user avatar
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3 answers
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Question about eliminating parentheses

Are '□(p → q)' and 'p → □q' semantically equivalent? Specifically, does eliminating parentheses in the former gives us the latter?
Edward Freeman's user avatar
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Trying to avoid a modal explosion: if anything can be obligated, and ought-implies-can, then would everything be possible?

Where by "anything"/"everything" I mean atomic propositions (and I am quantifying over atomic propositions). The argument would seem to be something like: ◊OBA, ∀anyA OBA → ◊A ◊◊A ...
Kristian Berry's user avatar
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4 answers
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Is Fermat's last theorem a logical necessity or a different kind of necessary truth?

Fermat's Last Theorem states that no three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2. The question was, is this a logically necessary ...
Vihan 's user avatar
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Proof verification of god existence theorem

NB: My question was closed on math stack exchange. They advised me to post it here, but due to the lack of LaTeX formatting, I had to upload it as images. Apologies for that. I am a first year student ...
dyy's user avatar
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Omniscience leads to necessitarianism

You have probably seen these types of arguments before on incompatibility of omniscience and free will. The question is are these arguments valid and what can be a good refutation? Let G= x is known ...
Vihan 's user avatar
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Does Necessity Mandate Uniqueness?

Suppose there is a nonzero number of contingent entities and a nonzero number of necessary entities. For example, the law of non-contradiction is probably a plausible candidate for something that ...
vicky_molokh's user avatar
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3 answers
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Is necessary existence a property?

If existence is not a property then doesn't it follow that necessary existence is also not a property? If it is then why?
Vihan 's user avatar
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Completeness theorem for QML. A doubt about the relation R in the canonical model. (constant domain)

I dont understand this script: wRv iff □−w ⊆ v, where w is a word of W, that is an Lc-saturated set (maximal consistent with the ∀-property, (C is the set of constants that we use to amply the set of ...
davide_cava's user avatar
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4 answers
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General sentence operators

There are lots of operators that act on sentences. Here are a few examples: P and Q not P forall x.P necessarily P eventually P x believes that that P it is obligatory that P etc. The first two ...
David Gudeman's user avatar
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Fixed/critical points of a nonexistence quantifier/function

Let j(∃0) = 1, and j(∃1) = 1, for a justification function j on ∃-sentences. So far, 0 is the initial critical point of the composite quantifier-function, and 1 is the initial fixed point. So let ...
Kristian Berry's user avatar
2 votes
2 answers
135 views

Can someone translate this into quantified modal logic?

So an attempt to translate- its not possible for two necessary beings to exist- in quantified modal logic. Is it correct? ¬◇∃x∃y[[□Nx ∧ □Ny] ∧ x ≠ y]
Vihan 's user avatar
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Interpretation of formula with free variables in QML with varying domain

The problem is known, both Huges e Cresswell (p.275) and Fitting e Mendelson (102) mention it. Example of the problem: we have a formula: □ (P(x) v ¬P(x)) that is true in the world w under the ...
davide_cava's user avatar
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How does Ulrich Meyer treat of an "at eternity" operator in temporal logic?

Something called a "book of abstracts TELS 2022" includes a summary of one Ulrich Meyer's essay on a topic in temporal logic: The challenge is to explain how eternal objects would differ ...
Kristian Berry's user avatar
3 votes
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34 views

What kind of homo/isomorphism, if any, applies to a certain pair of pairs of permission types?

The SEP article on deontic logic mentions at least once or twice that there seem to be two types of permissibility (also a difference between "ought" and "must," to note). Over the ...
Kristian Berry's user avatar
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1 answer
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If there is less than a 100% chance that X might occur, can it occur? [closed]

The key word is might. If there is a 100% chance that a thing might occur, that does not mean there is a 100% chance it will occur! It might not occur, even though there is a 100% chance it might ...
Brian's user avatar
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when A[t/x] it's false? It's to prove UI its valid in quantified modal logic with constant domain

Its for soundness theorem. I need to prove that the axioms (∀x)A -> A[t/x] its valid in constant domain semantics. I assume theres a world in a arbitrary model within (∀x)A -> A[t/x] its false ...
davide_cava's user avatar
2 votes
0 answers
85 views

A question on quantified modal logic

I originally posted this on math.stackexchange.com, but I’m cross-posting it since I know there are good modal logicians on here too. Also, I already asked a similar question here: Identity in ...
PW_246's user avatar
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4 votes
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Tautological Many Worlds?

this is my first question here so I hope I'm following the guidelines correctly. I recently found a relatively obscure physicist/philosopher who asserts that the concept of Many Worlds is ...
user's user avatar
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6 votes
3 answers
405 views

Implicit Models and Probability - are degrees of belief/truth/existence a complete free-for-all?

Or, to put it another way, as long as you model your statements using the grammatical framework of our modern logical idioms, is it appropriate practice to assign a probability to any utterance at all,...
Paul Ross's user avatar
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If we used √OB and √𝓐 operations, could we have a demi-is/demi-ought proposition that bridged full "is" with full "ought"?

The insight that the teleological ethicist seems to have is that final causality is a type of the moral law in the Kantian sense (from the second Critique): ... the moral law has no faculty but the ...
Kristian Berry's user avatar
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If existence-tropes would be absurd, does this count against trope theory or the theory of existence-as-a-property?

I advert to the word "trope" as used in philosophy and not as used in narrative analysis (although I can see a reflection of either sense of the word, in the other use). The argument goes: ...
Kristian Berry's user avatar
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22 views

Could a being be defined as such that its transworld identity is identical to its in-world identity?

I was reading through Collier[21], which is about Lewisian theism, alongside the SEP article on transworld identity, and have assumed that: The concept of transworld identity (TI) is not necessarily ...
Kristian Berry's user avatar
2 votes
1 answer
85 views

Is there a modal modification of the law of excluded middle that may render constructive?

Intuitionistic logic rejects the law of excluded middle, and paraconsistent logic rejects the law of non-contradiction. I wondered whether the rejected laws can still be incorporated, if they're ...
Dannyu NDos's user avatar
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80 views

√◊ (or generally √M, for whatever modal operator(s) M)

I tried Googling "demi-possibility demi-negation" and got nothing (just "demi-possibility" gave results mostly related to demisexuality). And my analysis of demi-negation didn't ...
Kristian Berry's user avatar
1 vote
2 answers
62 views

Does the claim of an is/ought gap presuppose relevance logic (at least for morality-talk)?

Imagine Hume's remarks but with reference to the usual disjunction introduction: In every system of conjunction, which I have hitherto met with, I have always remarked, that the author proceeds for ...
Kristian Berry's user avatar
1 vote
0 answers
37 views

Does "ought-implies-can" have to be taken for a universal material implication?

I was thinking of Quine's "change the logic, change the subject," saying, and thought over "change the deontic logic, change the deontic subject," and so then I wondered if deontic ...
Kristian Berry's user avatar
1 vote
1 answer
43 views

Is Aquinas' ethics a case of a supererogation-first system?

Section 2.2 of the SEP article on modal epistemology differentiates possibility-first from necessity-first systems. Per modal logic, one can take these as metaphysical readings of the order-of-...
Kristian Berry's user avatar
0 votes
2 answers
79 views

Computer Graphics Imagery (CGI) & Modality (Possibility)

The trend is obvious ... CGI is here to stay. Many movies wouldn't stand a chance in the box office sans computer generated images and I don't mean just the slew of superhero movies (DC & Marvel ...
Hudjefa's user avatar
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If Zalta objects exist, would there be a contingently abstract obligation?

One of the posits of Zaltaesque object theory (let's call it that, since there is something vaguely Kafkaesque about logicist realism) is that for every set of assertible encoding relations there is ...
Kristian Berry's user avatar
3 votes
2 answers
719 views

Can something be logically necessary now but not in the future?

Can something be logically necessary now but not in the future? I probably always assumed it couldn't, that it followed from the laws of logic alone, and that these are immutable etc.. I don't think ...
user avatar
2 votes
1 answer
93 views

Metaphysical indeterminacy and necessity

This is similar to my last question, but now I am asking about a specific/different interpretation of vagueness. To fit metaphysical indeterminacy into this picture Barnes and Williams [claim]... the ...
user avatar
3 votes
1 answer
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Can vague concepts have a modality?

Can vague concepts, which I am thinking of as concepts without boundaries, though there are I assume other ways of thinking about them, be necessary, especially if that modality changes? Supposing it'...
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Can we effectively (or at least plausibly) argue from a (3+)-valued set of deontic charges to 3+VL?

Suppose we defined an honest agent as one who intends to focus on stating truths, with liars as those who intend to focus on stating falsehoods. But if there are other relations an agent can bear ...
Kristian Berry's user avatar
1 vote
0 answers
19 views

Can physical universes nontrivially embed themselves into themselves?

Sometimes our world is said to be a "Big Conjunctive Contingent Fact" or that other possible worlds are "recombinations" of available propositions for some actual world. So model-...
Kristian Berry's user avatar
3 votes
1 answer
135 views

Modal system K - prove ⊢ (□p ∨ □q) → □(p ∨ q)

I am trying to prove the following: ⊢ (□p ∨ □q) → □(p ∨ q) However, I think that I am lacking the knowledge of a tautology in classical logic that would help me prove this. I tried something, but it ...
john doe's user avatar
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2 answers
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Axiomatically prove □(A ∨ ¬B), ¬□A, ⊢ ◇¬B in modal system K

This time I have a more "complex" problem at first glance. I need to create a direct proof using the axioms of system K and rules of inference, but I have been unable to do so. □(A ∨ ¬B), ¬□...
l0ner9's user avatar
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