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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If modal operators can be reduced to functions on conditional/disjunctive connective operators, what is the effect on the iterated-modality question?

Assumptions. The overall claim is that, "X is possible," when X is some proposition, can be translated into, "If X is the object of a true conditional or disjunction, then the ...
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Looking for help understanding modal logic and graph structure

I'm a novice to modal logic and only have a passing familiarity with classical logic. I started reading 'Modal Logic for Open Minds'. It is very readable, but then on page 16 the author introduces a ...
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Future tense explanations?

Is it possible to explain in the future tense? For example, "there will be smoke" because "there will be fire"?
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Modal logic for absoluteness

Modern modal logic has the modalities of necessity and possibility. However, both of these can be seen as relative to the set of possible worlds and the accessibility relation chosen for the semantics....
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Modal Logic: A Clarification

This is presumably an extremely basic question, but I didn't have any luck on my preliminary attempts to Google an answer or track one down here. After hearing a number of debates and presentations in ...
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How to accomodate hyperintensionality in a Bayesian framework?

Generally, propositions are modelled as sets of possible worlds, and Bayesians define a credence function on the set of those propositions. They then adopt new credence functions in response to new ...
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A "combining logic" moment in Kant

In "Ethical Theories and Moral Guidance", Pekka Väyrynen goes over proposals and arguments concerning the knowability of moral claims. Kant's relevant proposal (in the second Critique) is: ...
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Necessary and antipossible worlds?

So suppose that ☐A → ~(◊~A), but also that ◊A → ~(☐~A). Or, rather: ◊(☐A → ~(◊~A)) & ◊(◊A → ~(☐~A)) {i.e., either order of definition is itself possible} Maybe I'm being a fool, but I'm finding ...
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Comparing one modal interchange with another

In the normal systems of modal logic, you can have either of the following: Possibly X is defined as not necessarily not X Necessarily X is defined as not possibly not X I know this is not the same ...
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Looking for an introduction to "possible worlds" aimed at the deeply skeptical

NB: this question is a reference request. I have already read countless introductions to modal logic (the latest one being Chapter 10 of @PeterSmith's Beginning Mathematical Logic: A Study Guide1). ...
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Is there a notion analogous to “the inductive conception of set” in modal logic?

In many introductory treatments of modal logic, one defines a Kripke model with respect to some domain D. In variable domain semantics, each world in the Kripke model is assigned a different subset of ...
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What is ̚▢p equal to in modal logic? [closed]

I would assume ̚▢p= ◇p v ̚◇p, but I’m not sure.
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Causality and Modal concepts

I am a physics student but very interested in some topic of philosophy (specially in analytic philosophy). A question which have been struggled me for some time is the relation between modal concepts ...
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What is the philosopher's take on information and thermodynamic entropy?

So there are various interpretations of probability. Frequentism is the likelihood of events of say for example if I roll a dice the likelihood of of getting a 5 is 1/6 if repeated over and over. ...
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How to be skeptical of transcendental arguments?

SEP and others have transcendental arguments as claims “namely that X is a necessary condition for the possibility of Y—where then, given that Y is the case, it logically follows that X must be the ...
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Truth/actuality as an operator

Frege claimed that "it is true that" adds nothing to the actual meaning of an assertion, and following him along this line are prosentential theories of truth. However, I wonder if this is ...
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Kant's modal logic

It is customary nowadays to have the introduction rule for the possibility operator "◊" be a two-edged negation of the necessity operator "□": ◊A = ~□~A. It is also possible (haha!)...
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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, ...
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Introduction to Formal Metaphysics

As I am very interested in Edward Zalta's research in Axiomatic Metaphysics, I wanted to read up on Formal Metaphysics. Would there be some introductory material that would help? Thank you in advance ...
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How to prove, in modal logic, that □A→A is valid (T axiom) iff R is reflexive?

How to prove, in modal logic, that □A→A is valid (T axiom) iff R is reflexive? I'm not sure how to prove axiom in reverse?
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Axiom 4 in epistemic logic

In epistemic logic, axiom 4 says that if I know p, then I know that I know p. What is the philosophical value of such an axiom?
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Does ◇◇A mean ~◻~~◻~A? If so is it by definition or it requires a proof?

In system K, ◇A is defined to mean ~◻~A. Therefore, it is very tempting to conclude ◇◇A means ~◻~~◻~A. But I am not certain whether this is valid conclusion to make, because in ◇◇A, the main operator ...
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Proving ~◻p → ~p in System K [closed]

I am working on a proof of ~◻p → ~p in System K. It says "If it is not the case that p is necessarily true, then p is not true". I have turned all the abbreviated symbols into their ...
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Proving validity/invalidity of a modal argument

□(A v B) → (□A v □B) ...(1) This symbolic argument is intuitively invalid. In (1), if we replace B with ~A, then we see that though the antecedent is necessary, the consequent is a contradiction since ...
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What is the best place for a layman to learn about Modal Logic?

As stated in the title, I am interested in learning about Modal logic as a layman in the subject. I would appreciate any books, videos, articles, ect. Thanks!
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can S5 be the weakest logic?

If we were to prove that an argument is a logical truth only in S5 logic out of (K, T, S4, and S5). does that make S5 the weakest of these four logics in which the argument is a logical truth?
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How to define ‘impossible’ using propositional modal logic?

I am trying to define impossibility using the symbols we have in propositional modal logic. I got ‘negation diamond alpha’ in mind as equivalent to ‘it is impossible that alpha’. It that correct and ...
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Can Fregean sense of proper names be described in terms of intension?

If I am not wrong, the old Fregean distinction between sense and reference can be read in terms of a distinction between intension and extension: The star of the night and the star of the morning are ...
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Lewis argument to defend modal realism

In the fourth chapter of "Counterfactuals", David Lewis tries to justify his positions about modal realism. He claims that: "We might take them [modalities] as metalinguistic predicates ...
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Stances on possible worlds

Modal realism is the belief that all possible worlds actually exist. Actualism is the belief that possible worlds don’t exist at all. What are some examples of modal-metaphysical views which try to ...
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Natural Deduction in S5 Modal Logic - Introduction and Elimination Rules

Are there natural deduction rules for the S5 modal operators that mirror the introduction and elimination rules for quantifiers in predicate logic? I recall seeing somewhere rules like the following: ...
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Can you give me some concrete example, so that I could understand these modal logic sentences

So there is these simple modal logic sentences: □(a → b) and a → □b Can anyone help me with some real-life examples, because I have troubles grasping the difference? edit The simpler question is this: ...
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Is it possible to find a counter model for epistemic closure in Nozick's system?

The epistemic closure is that: If S knows (if p then q) then (If S knows p then S knows q). In Nozick's Truth-Tracking Analysis S knows p if and only if p is true S believes that p If p were false, ...
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Necessary possibility

One subsequence in the argument I'm working on goes something like this: ♢A → □♢A. ¬□♢A. ∴ ¬♢A. This seems valid (it's modus tollens, no?) but it seems to make the actual argument too "easy&...
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"Where" does the counterpart relation subsist?

AFAIK, according to the counterpart theory, it is true of me that I could have lived a different life, if my counterpart in another possible world did live a different life. But where is it true that ...
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Does the forcing phenomenon prove some sort of set-theoretic multiverse?

It seems that, "A can be forced to equal B," allows, "A is possibly equal to B." In possible-worlds lingo, this gets us, "There is a possible world where A = B." Since ...
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Can truths about the natural numbers vary across possible worlds?

The truths of logic are the same in all possible worlds. However, what about truths about natural numbers? Like, for instance, is there a world where there are only finitely many primes, or a world ...
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How do you reduce repeated modality in S5?

Kenneth Konyndyk's Introductory Modal Logic claims (p. 55) that all formulas in S5 with a modal degree greater than 1 can be reduced to degree 1. By degree, he means the maximum number of modal ...
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Is modal logic too coarse-grained? [closed]

Modal logic has "necessary" operators (true in all worlds) and "possible" operators (true in some world). Compare this to probability, where only probabilities of 1 would be "...
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Possible worlds semantics for quantifiers

In possible worlds semantics, sentences are associated with propositions, i.e. a set of possible worlds in which the sentence is true. For sentences like, "There is an x such that x is F", &...
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What is 'expendable' in logic and how to explain 'tautology' given this image?

This image is from http://www.nfillion.com/index.php/teaching/9-logic-112. According to this, a proposition can have 4 basic properties: (1) necessarily, (2) not possibly, (3) missing, and (4) ...
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Is it consistent to say "X is possible but false"?

Is it consistent to say something like "Possibly there is a cat in my room, but in fact there is not"? Basically, is it consistent to assert that something is possible but in fact not the ...
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How to make sense of " I know that p but I could be wrong as to p"? ( Faillibilism)

There is a well known modal fallacy regarding knowledge which says that if some subject s knows that p, then p cannot be false, and therefore , p is a necessarily true proposition. Source : [ by ...
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Is there a non-transitive frame in which schema 4 is true? Or an irreflexive frame in which schema T is true?

So, I know that I can construct a frame {W, R, I} which is not transitive and in which schema 4 is not true (more specifically, Axiom Schema K and Axiom Schema 4 are not both true). I also know that I ...
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Yablo's condition on "Truth about a subject matter"

In section 2.4 of "Aboutness" Yablo offers the following analysis of what does it mean that a statament is true about a certain subject matter/topic: So, what is the proposition we are ...
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Are there any philosophers who are experts on conceivability and have written texts about it?

I recently asked about a definition of conceivable. Now I am asking a slightly different question. I want to know if there are philosophers who have written texts clarifying (and perhaps even defining)...
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Prove that p → □p is not derivable in system K?

The only way I could think of doing this is to show that p → □p with the K axioms would imply a contradiction, but I don't think that's true. Not sure how to get started on this. Do I just have to ...
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Possibly necessarily P → Necessarily P?

So I saw this proof for ◊□p → □p but I don't know if it's true. ◊~p → □◊~p (5 axiom) ◊~p → ~◊~◊~p (Definition of □) ~~◊~◊~p → ~◊~p (Contraposition) ◊~◊~p → ~◊~p (Double negation) ◊□p → □p (Definition ...
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Modal Logic Proof in System T

I need to provide an axiomatic proof of the following formula in System T of modal logic: ◇(A→□B)→(□A→◇B). Any advice on how to start would be great!
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In the ontological argument, can the existence of an MGB be rejected as provably false?

There are a lot of slightly different formulations of the ontological argument for God, but I'm going to use William Lane Craig's phrasing of Plantinga's, because that's the version I first heard. His ...
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