# 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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### 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 ...
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### If it is not possible that p is not possible in K, does it follow that p is possible in K?

I have the following question. If it is not possible that p is not possible in K, does it follow that p is possible in K? Thanks in advance!
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### How to generate counterexamples for modal logic trees from Girle

I am having a heck of a time understanding a counterexample discussion in Girle 2000. Here is the tree: But then, on p. 40, Girle reads off the tree: I understand where the values in k and l come ...
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### How to prove □ φ ↔ ◊ □ φ

I am looking for a proof of the formula □ φ ↔ ◊ □ φ (a theorem in modal logic S5) How can this theorem be proven from the axioms of modal logic? It makes some intuitive sense to me, as something that ...
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### Logic Expressions and Notation

I am brand new to logic so am trying to teach myself how to write logic expressions. Let's say I take the following Modal ontological argument: -Premise 1: It is possible that God exists. -Premise 2: ...
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### Is modality always involved when we talk about the future?

When I make statements about causes in the future like "Cold causes frost to form on the window.", am I unavoidably involving modality even though i'm not using modal auxiliaries? Can ...
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### The intensionality of modal logic

What exactly makes modal logic intensional? In what follows, for illustration, I will focus on propositional modal logic (MPL). I know that the modal operators in MPL are intensional since the truth ...
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### Does the Principle of Sufficient Reason imply everything is necessary?

Leibniz's Principle of Sufficient Reason (PSR) states that: for every fact F, there must be a sufficient reason why F is the case (https://plato.stanford.edu/entries/sufficient-reason/#WhatSuffReas). ...
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### If it is possibly good that the world actually exists, is it actually good that the world possibly exists?

Note: the question involves some version/vector of the Barcan formula, albeit with the existential quantifier swapped out for an actuality operator (possibly on terms under propositions rather than ...
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### Which of these distinctions in modal terms overlap each other (if any)?

Ori Simchen is an author who has published work on analysis of a difference (sustainable or not) between general and particular possibilities. Something is particularly possible when it is possible &...
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### Are there "merely necessary" worlds?

If whatever is actual is possible, but not everything that is possible is also actual, and if everything that is necessary is actual (and hence possible), it looks like it might not make sense to talk ...
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### Are there any established logical symbols for merely possible and contingently true?

In modal logic we have: P → ◇P - If something is true, then it is true at some possible world. ◻P → P - If something is necessarily true, then it is true. However, the reversed conditionals don't hold ...
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### Is division of propositions by their modality comprehensive?

I call division of any concept comprehensive if the combination of concepts received by such division has a scope congruent (containing exactly the same objects) to the scope of the divided concept. ...
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### How does modal logic address this equivalence?

I was picking where to eat dinner, and this logic question arose. Because I didn't want to dine at the same place twice in a single day. Let me call the restaurant "Kim's". The following ...
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### Questions about truth in deontic logic

I'm currently studying a bit of deontic logic due to a course in modal logic that I'm taking and I have some questions. My main question is regarding truth value in deontic logic. Initially, I ...
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### What does this phrase mean according to the Modal Epistemic Model of logic?

According to the modal epistemic theory of logic, what does the statement P over P...ie p/p = p Np? To clarify, I am asking in the context of this document, because it seems to use Np meaning not p, ...
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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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