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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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 ...
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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 ...
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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 ...
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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,...
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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 ...
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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:
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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 ...
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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 ...
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√◊ (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 ...
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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 ...
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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 ...
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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-...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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-...
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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 ...
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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), ¬□...
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Proof of □P ⊢ □¬¬P in modal logic system K
I need to prove the aforementioned formula in modal logic system K, which I am having trouble to do.
Of course, this should be easy to prove if I had access to axiom T, but since it's system K, we can ...
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Modal Companions and Trivially Strict Conditionals
The classical material conditional is given a truth-functional definition that can be determined with truth-tables. Intuitionistic implication is a kind of strict implication that can be translated to ...
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Infinitary modal logic
Let 'L' and 'M' denote the necessity and possibility operators. In Modal Logic, the following theorems hold:
L(p and q) <--> (Lp and Lq)
(Lp or Lq) --> L(p or q)
M(p or q) <--> (Mp or ...
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platinga's actualism and introduction of essences
I am reading Plantinga's "Actualism and Possible Worlds" and I am struggling to see why he needs to introduce his idea of essences to resolve the following issue:
The actualist holds that:
(...
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A question about David Lewis's refutation of taking possibility as consistency
I’m reading a chapter from David Lewis’s counterfactuals. He says something which I’m confused about, wondering if any of you guys can explain what he's saying...
“ We might take…. ‘Possibly P’ [to ...
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Are there "generalized Barcan formulas" in combining logic?
I did a search for "epistemic Barcan formula" and got only one result, with the sample being:
An example with the Barcan formula in an epistemic context shows that our intuitions are
much ...
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Entry points from philosophy into mathematics at higher levels?
Everytime I look up of the link between philosophy and mathematics, I see the topics only of the most foundational levels discussed. As in logic, and stuff. When I study higher mathematics theories, ...
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What is a “possible” event?
Things seem to happen or they don’t. If a dice rolls on 6, does this mean that it could have been possible for it to land on 1-5? We seem to differentiate this kind of event from an “impossible” kind ...
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Is Neil Barton's algebraic/ontological distinction equivalent to the actualist/possibilist distinction?
In, "Multiversism and Concepts of Set: How much
relativism is acceptable?" Neil Barton distinguishes between an ontological interpretation of set-theoretic multiverses as referents and an ...
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Why shouldn’t I be a skeptic about the Necessitation Rule for alethic modal logics?
Alethic modal logics for metaphysical possibility and necessity usually have the Necessitation Rule:
From ⊢P, infer ⊢□P.
Doesn’t this commit us to the meta-notion that logical necessity modulo some ...
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Is there a system of logic which denies DNI?
From what I know, the law of double negation is often simplified as p <=> ~~p. Intuitionist logic splits the biconditional into DNI and DNE.
DNI: p -> ~~p
DNE: ~~p -> p
and denies DNE ...
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Are there modal operators that don't take a proposition as an argument?
All of the modal propositions I can think of are most reasonably analyzed as a modal operator applied to a proposition, and possibly other arguments. In the following examples, I'll write the ...
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Why does no modal logic use an anti-symmetric (partial order) accessibility relation?
Several sources includes catalogs of many modal logics, often arranged into a lattice of inclusion, showing increasing power, from K to S5. Naturally, for each logic there is a corresponding ...
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Why is "Water is not H2O" False in all possible worlds?
I am reading Chalmers' "Two dimensional semantics" and "Two dimensional argument against materialism" and a point is unclear: As per Kripke (1980), "Water is not H2O" is ...
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deontic logics without agency
Standard deontic logics are agentless. That is, obligations in the logic are not assigned to agents; instead, they are made sort of general and ephemeral. This strikes me as rather fraught with all ...
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Obligation and material implication
Deontic logic often contains the axiom
□(p → q) → (□p → □q)
where □ is being used for "it is obligatory that".
This axiom strikes me as odd. It reads "If it is obligatory that p ...
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Actual content of Gettier cases
I'd not rewrite here classical Gettier cases.
Each of cases hinges on a crucial fact: after obtaining "knowledge" from observable facts via disjunctive introduction or entailment, the ...
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Identity in Quantified Modal Logic
Why is ¬(◇(a=b)∧◇¬(a=b)) a validity in Quantified Modal Logic (QML)? For example, let a:=“the present King of France” and b:=“the richest bald person alive”. Then, it seems ◇(a=b)∧◇¬(a=b) is not a ...
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Proving IMPLIES IDENTITY in David Beaver’s dynamic semantics
Consider this principle, the Beaver analogue of the validity “if φ, then φ”:
σ[φ implies φ]σ
L0:{atom, not, and, implies}
L1: {atom, not, and, implies, ∂}
L2:{atom,not,and,implies,□,♢}
Prove IMPLIES ...
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Is there a name for the relation between a proposition and the proposition formed after applying the diamond modal operator?
I don't know if there is a name for it but, since a negative proposition is the negation of another proposition for e.g. the proposition that "it is not the case that it is sunny" is the ...
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Help with questioning the modality of a proposition
If we have a statement like "it is possible and obligatory that the man is eloquent.", does it make sense to ask a question like "Why is it possible and obligatory that the man is ...
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Zero-one laws Model Logic, question regarding significance of domain size
Wikipedia informs me that:
Essentially (correct me if I'm wrong) the result states that as the domain of objects (domain of discourse) grows (n->inf), a static first order sentence (S) will be ...
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Zero-one laws and Modal logic, question regarding statement of result
Wikipedia informs me that the probability that a given structure (G-subN) with Domain {1,...,n} models S where 'S' is a first order sentence converges to either 0 or 1 as n->inf.
I have two ...
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Does determinism require Modal collapse?
The question is pretty much self-explanatory, I was just curious if there is any possible way to show that Modal collapse isn't caused by determinism.
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An introductory book on philosophy of language and logic?
I tried self teaching philosophy of language, logic, modal logic but I am lost as a headless chicken. Can anyone help me please? I have a full time job, but I can take an hour everyday and learn a bit....
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What's the constructivist's view to the S4 modal logic?
Intuitionistic logic can be translated to S4 modal logic by parsing intuitionistic P→Q to classical □(P→Q). There is no other way round, for there is no intuitionistic equivalent to ◊P. To analyze ...
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How to prove that: ⊢/k ◻p v ◻¬p
My though it that we can refer to completeness. So just argue that ◻p v ◻¬p does not have a corresponding model. But I am not sure...
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How to prove ◻(ϕ → ψ) → (♢ϕ → ♢ψ) a theorem of the normal modal logic S5? [closed]
I feel like this is the inversion of logic 5, so my intuition is that we cannot prove it a theorem of logic 5... But I am not sure at all
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A question on the belief operator in Doxastic Logic
Let Bp be the statement "it is believed that p".
Why is ~Bp not equivalent to B~p?
in words it amounts of saying that: "it's not believed that p" equivalent to "it's believed ...
