# 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 ...
55 views

### 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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### 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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### 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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### 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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### 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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### 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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### circularity of possibility defined over possible worlds

I have just checked similar questions that have been asked(and answered) before but I am still confused. How is it that the notion of possibility defined over as being True in some possible world not ...
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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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### 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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### 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 ...
1 vote
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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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### What is the Barcan Formula?

can someone please help explain this Barcan formula to me? (In English translation and maybe with an example?) (◊ ∃x Fx) ↔ (∃x ◊ Fx) And if there is only one possible state of the world, would it ...
1 vote
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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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### 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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### 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 ...
1 vote
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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!)...
359 views

### Does it hold that everything exists necessarily?

In Quantified modal logic, "constancy’s defenders can point to certain powerful arguments in its favor. Here’s a quick sketch of one such argument. First, the following seems to be a logical truth: ...
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### A possible formal failure made by Kripke?

In Kripke 's Naming and Necessity, there is a footnote says that "Lewis's elegant paper also suffers from a purely formal difficulty: on his interpretation of quantified modality, the familiar ...
1 vote
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### Exercise 2.2b from A New Introduction to Modal Logic

I am kind of stuck on page 48 on exercise 2.2b in Hughes and Cresswell; In case you don't have the book at hand here's the question: Let K** be K but with N and K replaced by LT: L( p→ p), R*: ⊢ a → ...
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### Does this modal ontological argument prove the existence of God?

What are some objections to this form of the argument? It seems like the only premise that can be disputed is premise 1, but nobody has successfully disproven the possibility of a maximally great ...
1 vote
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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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### 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, ...
1 vote
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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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### 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 ...
1 vote
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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 ...
1 vote
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### What is the literal meaning of "The only thing that I know is that I know nothing"? (Is not knowing anything a knowledge?)

If a person says, "The only thing that I know is that I know nothing." What exactly does that mean (not metaphorically), literally? If the only thing they know is that they know nothing, ...
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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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### 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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### 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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### Does the finitary proof of the consistency of relevant PA shows that first order PA is irrelevant?

Relevance logic takes a closer look at the implication operation in first-order logic. It suggests that implications such as: p and not p -> q cannot hold; in ordinary English, an example of this ...
1 vote
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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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### Is there any way to represented nested modalities in alethic modal logic?

It is possible to represent simple statements involving possibility and necessity in alethic modal logic and possible world semantics. But consider a statement like "It is possible that it is ...
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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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### How to prove that the axiom H is valid in the following frame

To prove incompleteness of KH, I have to prove that the axiom H is valid on the following frame: Axiom H goes as follows: □(□p↔p)→□p I don't know how to prove this, but here's one idea that's half ...
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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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### How to read modal logic's countermodels?

I'm new to Modal Logic and currently playing a tree proof generator just to see how some stuff work, but I can't read the countermodels that the algorithm gives me when my proposition is invalid. I (...
1 vote
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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 ...
1 vote