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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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Equivalence of strings of modal operators in modal logic

I'm trying to solve a question which asks me to show that for any two finite strings O₁ and O₂ of □s and ◊s, (e.g. □□◊□◊□), that i) if O₁≡O₂ then OO₁≡OO₂ and ii) if O₁≡O₂ then O₁O≡O₂O where O is ...
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Logical expression that non-existent things don't do anything?

How could we express the idea that "something that doesn't exist cannot possibly do anything" using a logical argument? And if so, it is at all possible to prove that kind of proposition?
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Semantic expressiveness of modal logic

I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself: P1 ◇ ∀a, ∃x // GNB(x, a) ∧ ...
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Questions from a new introduction to modal logic by Hughes and Cresswell

I just want to see if I got this correct. Show that the following wff is valid in every seating arrangement: Mp -> (Lq->Mq). Here's my argument: Assume player A sees at least one player B that ...
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How to express that something that exists is possibly necessary in Modal Alethic Logic?

Suppose that A is True (like 1+1=2) , then how to formulate this proposition in Modal Alethic Logic? If A is the case, then it is possible that A is necessarily the case. For example : If I am ...
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61 views

Going from ◊(∃x)◻Fx and ◻(∀x)(Fx --> E!x) to ◊(∃x)◻(Fx & E!x)

Is it a valid inference (in, say, any quantified modal logic S5 system) to go from ◊(∃x)◻Fx and ◻(∀x)(Fx --> E!x) to ◊(∃x)◻(Fx & E!x)? (E!x is the existence predicate, by the way.)
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Validity of a modal argument?

Would you say that the following argument is valid? And if not, why exactly? For all we know, A may be the state of B; What C does is determined by the state of B; Therefore, for all ...
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211 views

A problem with Modal Logic (necessary truths)

I have this problem with Modal Logic that I am not sure I see which propositions in this logic are necessary besides tautological propositions. I mean metaphysically, something is necessary if it's ...
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Counter-examples in modal logic

I’m getting stuck on counter-examples to formulas in modal logic. I’m now doing the exercises in Girle’s Modal logic and Philosophy, 3.4.1. Let’s take (a), since the answer to that one is given. The ...
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141 views

Negation of a E quantifier in a Modal Logic T System?

In System T its possible to conclude: (1) □Ex->Ex Therefore its possible to conclude: (2) Ex->◊Ex But whats the result, if I negate the existence quantifier? Is it: (3) ~Ex->~◊Ex or is it: (4) ~Ex->◊~...
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134 views

On that p does not imply necessarily p

Am I right to assume that in no modal logic, whether in K or in a logic where the accessibility relation is specified as either reflexive, symmetrical or transitive, does ”p implies necessarily p” ...
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95 views

How to prove or disprove “Necessarily P entails P” in Kripke Modal Logic?

I'm doing the body of exercises in Priest's Introduction to Non-classical logic, and got weirdly stuck on 2.12 (o). (I'm on Problems 2.12, if anyone has a link to the answers that would also be much ...
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184 views

Axioms for modal logics based upon counterfactuals

Suppose we have a logic for counterfactuals as with David Lewis. I here use ⇛ for the counterfactual conditional. So suppose we have: Rules: (1) If A and A→B are theorems, then B is a theorem. (2)...
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Conditional logic - how to apply a conditional with complex antecedent in tableaux?

I'm referring to the conditional logic of C+ as described Graham Priest in "An introduction to non-classical logic" chapter 5, where the strict conditional is enhanced with ceteris paribus, and a ...
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94 views

Are there logicians who argue that knowing and believing are NOT amenable to formal study via modal logics?

Vincent Hendricks and John Symons notes the following about epistemic logic: Epistemic logic gets its start with the recognition that expressions like ‘knows that’ or ‘believes that’ have ...
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What's the difference between logical modalities and physical modalities?

I am just wondering what's the difference between the two. I would say that there is something different, but honestly I can't define what it is exactly. What do you think?
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How do pragmatists avoid this modal argument against their view of truth?

I am reading Harry Gensler's Introduction to Logic (Routledge, 2002) and doing exercise 1 of 7.3b in the "Basic Modal Logic" chapter. I think I follow the steps. The answer is in the book. My ...
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Propositions that can't be used to distinguish possible worlds

Are there known ways of formalizing the notion of propositions that can't be targeted by counterfactuals in a coherent way? Or of propositions that are outside the scope of the framework in question? ...
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3answers
262 views

Are all logically necessary statements self identity claims?

When we say that x is necessarily P, are we not asserting that this is the case regardless of all contingent facts, so regardless of what x and P are? And if x was P regardless of what x and P are, ...
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1answer
213 views

What the main reason for Bertrand Russell's skepticism and rejection of modal logic?

It seems to me that Bertrand Russell was somewhat hostile to the idea that modality plays a role in logic.
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258 views

What is necessity in modal logic?

I understand that something that is necessary must exist. However, what is the exact definition of necessity? Thank you.
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152 views

Does anyone have a proof checker they prefer using for modal logic?

I am looking for a proof checker for modal logic using natural deduction or sequent calculus. I am trying to learn Isabelle, but I think there should be a simpler solution. Although I can rely on ...
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349 views

Can possible-but-non-actual objects have accidental properties?

The modal logic I am considering is the "Simplest Quantified Modal Logic" which combines first-order predicate logic with identity, with S5 in the most straightforward way, described here and slightly ...
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4answers
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How to denote physical (not logical) impossibility in modal logic?

Say I want to note that in this world, it's physically impossible to jump over the Eiffel Tower. I can just write ¬◇x, but this seems to say that in all possible worlds x is impossible, and I want to ...
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67 views

introduction to modal logic

I am not entirely sure if we are allowed to ask such questions here but I was wondering if anyone could suggest me a real introductory level textbook on modal logic
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How many equivalence classes does the accessiblity relation have in S5?

I'm a math student taking philosophy classes. So I have some math background but am absolutely unfamiliar with metaphysics&c. Recently I've come around the "Nothing Is Impossible" paper as a part ...
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Logic and resolving a modus tollens

Wasserman presents a common argument against time travel: (P1) If backward time travel were possible, it would be possible to perform a self-defeating act. (P2) It is impossible to perform a self-...
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In modal logic, why not 'possibly p' → 'not necessarily p'?

I'm told that if ◇ means 'possible' and ◻ means 'necessary' and ~ means 'not' and ↔ means 'if and only if', then ◇P ↔ ~◻~P I get that if it is not necessarily not going to be sunny ...
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Establishing validity of ◊(∃x)◻[(E!x ⊃ Ox) & E!x]/ ∴ (∃x)◻[(E!x ⊃ Ox) & E!x]

I was wondering under which sort of quantified modal logic S5 system would the inference from ◊(∃x)◻[(E!x ⊃ Ox) & E!x] to (∃x)◻[(E!x ⊃ Ox) & E!x] be valid. Would this require a constant domain ...
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Justification for axiom OB-RE in deontic logic

Let OB p denote "p is obligatory". Axiom OB-RE is (p ↔ q) → (OB p ↔ OB q). This axiom seems false to me (under the interpretation of obligation). For example, let p denote "don't lie to me" and q ...
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The converse to the C modal logic axiom - has it been studied?

There is a C axiom as mentioned at https://plato.stanford.edu/entries/logic-modal/#MapRelBetModLog in Section 8. My question is: what can be said about the formula which is the converse of the C axiom?...
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How to construct a counter-model of □P --> □◊P in T and K?

I am new to modal logics and would really appreciate it if someone would be able to help me out with this practice question. I’ve established the validity theorem in T with an axiomatic proof, but I ...
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128 views

If I cannot draw a world in a truth tree in modal logic does that mean that no other worlds exist for that statement?

Suppose I have a truth tree for a modal logic statement that is closed or is open but for which I cannot continue drawing worlds, does that mean that there are no other accessible worlds in that modal ...
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249 views

What is the counterexample in modal system K for “⬜A ➡A”?

As I understand it from Modal Logic 2.1 - the systems M, B, S4 & S5, I should not be able to show "⬜A ➡A" in modal logic K. The following truth tree seems to confirm this, if I did it correctly: ...
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179 views

Why can one not draw a world in modal logic given necessity?

In Modal Logic 1.2 -- truth trees for K about 1:30 into the video, the presenter said: If you have possibly A then you need to draw an arrow to a new world and derive A in that world because w0 ...
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What is the justification for closing a whole branch in a modal truth tree diagram if there is a contradiction in only one world?

I am watching "Modal logic 1.2 - truth trees for system K" presented through Kane B's channel. The standard propositional truth tree diagrams are not a problem. Where I am having trouble is opening ...
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Why might truth imply necessity?

It seems well established (or, well-accepted) that necessity implies truth. For instance, in a context of epistemic logic, if one knows A, then A is true. On the other hand, I found on the Internet ...
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326 views

Natural deduction introduction and elimination rules for modal quantifiers

I've read several papers on modal natural deduction but I've only been able to find one clear explanation of []-Introduction ([]A if A can be proved from no assumptions/premises). But there were no ...
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Nonexistence and invalid formulas in modal logic

In first-order logic, I can essentially just ignore issues related to nonexistence and invalid formulas, without losing much. There is also free logic, in case I'm not happy with simply ignoring these ...
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46 views

How to translate classical logic to basic Kripkean logic?

I'm trying to semantically prove the following argument (sorry about the formatting - I'm new to stackexchange): if P ⊨c Q then ⊨k 򪪪(P → Q) However, I don't know how to translate or relate the ...
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791 views

What determines accessibility of possible worlds?

Recently, I have begun studying modal logic, using Brian Chellas's Modal Logic: An Introduction. Something keeping me from fully understanding the material is the idea of a possible world. They seem ...
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Rigid designators, equality and functions in many-valued logic and (simple) quantified modal logic [closed]

After reading "In Defense of the Simplest Quantified Modal Logic", I wonder how to add functions to the language of the simplest quantified modal logic (QML for short). The simplest model of QML has a ...
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615 views

Is there a name for each individual's perceived sphere of reality?

Is it an acceptable idea that each individual carries their own model of reality in their mind? Is there a name for the model that each individual uses to perceive reality? Is there a name for the ...
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Why does modal logic need to use ◻◻p?

In Frederic Fitch's Symbolic Logic he proves (11.8, page 66) that "◻p" coimplicates "◻◻p". In 11.10 (page 66), he writes, A system almost the same as the system Lewis calls S2 is obtainable by ...
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Is there such a thing as provability of provability?

Gödel says that there are true statements that can't be proved, given a sound axiomatic system. Does anyone say anything about the provability of the provability of statements? Is it still an open ...
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330 views

How does negation operate in modal logic?

I was mulling over this proposition: Just because something is provable doesn't mean that it is important; and wanted to consider its contrapositive. How would I write this in formal (modal) logic? ...
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Why did many valued logic fail in describing modal logic?

The SEP article on many valued logic makes the following statement: The introduction of systems of MVL by Łukasiewicz (1920) was initially guided by the (finally unsuccessful) idea of ...
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What is Quine's perspective on probability?

I am curious about what Quine's perspective on probability may be and if we can say that the quinean viewpoint on modality can be considered similar to his viewpoint on probability. Is probability ...
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4answers
699 views

How can a tautology not be necessarily true?

My logic/philosophy exercises include the following statement: "Every tautology is knowable a priori but not every tautology is necessarily true." I'm bamboozled. How can a tautology not be ...
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How does the concept of the 'virtual' (Deleuze) relate to 'counterfactuals' (Lewis)?

We read: "[...] Deleuze will reject the notion of the possible in favor of that of the virtual. Rather than awaiting realization, the virtual is fully real; what happens in genesis is that the ...