Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

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

Filter by
Sorted by
Tagged with
-2
votes
2answers
107 views

Modal Logic: One non-transitive frame where schema 4 is invalid?

I know that schema 4 defines the class of all transitive frames, meaning that it is not valid in at least one model that is non-transitive. However, I am not sure how we would go about proving that if ...
1
vote
1answer
54 views

Do possible worlds partition the set of all possible states of affairs?

Let S be the set of all ( logically) possible states of affairs ( I could have said " events" or " propositions" maybe). Let R be the relation : state of affairs x is compossible/ compatible with ...
0
votes
1answer
102 views

How to prove rigorously that “ necessarily ( A OR ~A) ” does not imply “ necessarily A OR necessarily ~A”?

In De Interpretatione , Aristotle criticizes logical fatalism ( a metaphysical doctrine professed in the Megarian School, in particular by Diodorus Cronus). Aristotle reconstructs the reasoning of ...
1
vote
0answers
77 views

Modal Logic: Proving Schema Validity

When faced with a question of the sort, "Is schema X valid in class of frames C?", we usually go about proving or disproving this by assuming the antecedent of X and showing that the consequent ...
0
votes
1answer
92 views

Trying to formalize a certain sentence in predicate modal logic

I have the following sentence which I want to formalize in predicate modal logic. Let me know if it's correct or not. The sentence is:" What is good for you is not necessarily good for others". My ...
2
votes
1answer
95 views

Modal logic: Why is K5 determined by the class of all Euclidean frames?

I am interested in proving that K, the smallest normal modal logic, in combination with the formula 5 (Possibly A then Necessarily Possibly A) is determined by the class of all Euclidean frames. For ...
0
votes
1answer
89 views

What kinds of proofs can be given for axioms, e.g. the modal axiom S5?

From John Bigelow and Robert Pargetter's book, titled, 'Science and Necessity', they assert the following: . . . . The resulting system, S5, contains all the theorems of S4 and all the theorems of ...
-2
votes
2answers
96 views

Probabilty and QM [closed]

What has been written so far on the theme?
0
votes
1answer
75 views

Modal Logic: Why are Universal frames a subset of Equivalence frames?

I'm looking through the lecture notes for my course on modal logic and am having a hard time understanding why it is that U, the class of all Universal frames, is a subset of E, the class of all ...
2
votes
1answer
79 views

Modal Logic: Point-wise equivalence vs. (simple) equivalence

I am reading Brain Chellas' Modal Logic and have a question regarding point-wise and (simple) equivalence: what is a scenario in which two models are equivalent but not point-wise equivalent? Say, ...
0
votes
0answers
56 views

Is this valid in first-order modal logic?

(∀x)(∀y){(xEy) --> (∀z)[Tz --> (C(x,z)Ey)]} (Premise) {(∀y)[Ty --> (∃x)(Tx & xEy)]} --> {(∀y)[Ty --> (∃x)(Tx & xEy & ◻(Tx --> Ty))]} (From (1)) I'm trying to work this out in a quantified ...
1
vote
0answers
30 views

Did Carnap propose some kind of Modal Realism?

I have read in several pages that Rudolf Carnap, just as David Lewis (The creator of Modal Realism philosophical hypothesis) proposed that every logical proposition exists as a universe But is this ...
0
votes
1answer
33 views

David Lewis and naturalism

I am studying Lewis and I am wondering what are the cornerstones of his philosophical perspective. In particular, I am wondering if Lewis is a naturalist like his supervisor Quine.
0
votes
1answer
111 views

What are the various interpretations of modal logic?

Wikipedia lists the following interpretations of modal logic: Alethic: fundamental conditions of possible worlds, causality, time-space parameters, and the action capacity of persons. Indicates the ...
4
votes
1answer
62 views

What are good sources on vivid designators?

Wikipedia lists a vivid designator as the following: Vivid designator: In modal logic and the philosophy of language, a vivid designator is a term which is believed to designate the same ...
-1
votes
3answers
63 views

A question about possibility

If A, then B ~ A So, possible that B Valid or not? My take: Not valid. Reason: Valid means if all the premises are true, the conclusion must be true That means adding new information should not ...
2
votes
1answer
104 views

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 ...
2
votes
0answers
51 views

Can a Rigid Designator still exist if there is only one possible world?

According to Kripke, a rigid designator is a pronoun (but not all pronouns are rigid designators) and they pick out the same unique individual in each possible world. I understand this, however, if ...
1
vote
0answers
83 views

How and why Aristotelian essentialism is a problem for Quine?

I cannot understand how and why the Aristotelian essentialism is problematic for Quine. I have tried to read articles on the theme but probably I am not smart enough to understand them. Could you ...
2
votes
0answers
120 views

Modal logics - philosophical paradoxes using modeling by possible worlds

I'm searching for "paradoxes" in classical modal logics, meaning lines of reasoning which give a counterintuitive conclusion if performed in classical logic, which can be modelled by the (semantical) ...
3
votes
0answers
52 views

De Re, Counterfactuals, and rigidity

This is going to come off as vague or obscure; but, I hope the idea is performatively expressed: Two questions: Do you think that Kripke would argue that the impossibility of de re counterfactuals ...
2
votes
0answers
75 views

Does ◻(∀x)[Px ≡ ◻(E!x → Qx)] and ◻(∀x)(Qx → ◻E!x) entail ◻(∀x){Px ≡ ◻[E!x & (E!x → Qx)]}?

Say we are working in a free quantified modal logic system S5. Would the following argument be valid: ◻(∀x)[Px ≡ ◻(E!x → Qx)] (Premise) ◻(∀x)(Qx → ◻E!x) (Premise) ◻(∀x){Px ≡ ◻[E!x & (E!x → Qx)]}...
3
votes
1answer
259 views

How to prove □Q from P→Q and □P?

Given P→Q, and □P, in what systems can we conclude □Q? I want to know in which system the consequent is derivable from the premises and in which it is axiomatic (or perhaps we can include it as an ...
7
votes
2answers
298 views

Should truth entail possible truth?

It is a well-accepted axiom of modal logic that truth implies possible truth. Is there any philosophical argument against this conclusion? In other words, should truth entail possible truth?
3
votes
1answer
83 views

Is □(□A→B) v □(□B→A) provable in S5? If it's not, I am having trouble coming up with a countermodel

Modal Logic question about provability/ countermodels.
1
vote
3answers
183 views

Is anything not proven impossible therefore possible?

Is it a truism that, except for that which is proven impossible, everything is or must be considered possible? If so, why? It seems to me to be an argument from ignorance to say that just because we ...
2
votes
1answer
86 views

How to prove or disprove validity of ◻◻p → ◻p in the frame (Q,<) of the rational numbers with the usual less-than ordering?

I was wondering if someone can perhaps help with this proving. I am not sure how to handle a temporal frame that is not a set of only natural numbers. Any suggestions? Thank you.
2
votes
1answer
72 views

Is ◻((◻(P → ◻P)) ↔ (◻P v ◻~P)) derivable in S5?

Is ◻((◻(P → ◻P)) ↔ (◻P v ◻~P)) a theorem in S5? If so, is it also a theorem in B or just S5?
2
votes
2answers
151 views

Prove or disprove ~◇◻p → ◇◇~p in system K

How to start with the following proof? Any help would be appreciated. I have tried by assuming the left side is true, however, I get confused with the negation. ~◇◻p → ◇◇~p
4
votes
2answers
397 views

Does S4 (and B) hold for the strongest interpretations of ♢ and □?

Suppose these are the interpretations we are working with: ♢Ψ iff no explicit contradiction can be deduced from Ψ in FOL or in other words it's not provable that ~Ψ in FOL. ~♢Ψ iff an explicit ...
2
votes
1answer
40 views

Prove the rule that proves X(P) from X(a) preserves derivability in modal system K

I'm trying to solve a problem which asks me to show that the meta-rule defined by deriving X(P) from X(a) preserves derivability (i.e. if ⊢X(a) then ⊢X(P) in modal system K, where a is a sentence ...
3
votes
1answer
177 views

S5 proof of ⊢◻(◻P→◻Q)∨◻(◻Q→◻P)

I'm trying to construct an S5 proof of ⊢◻(◻P→◻Q)∨◻(◻Q→◻P). I know that ϕ∨ψ is equivalent to ~ϕ→ψ, and so what I'm really trying to derive is ~◻(◻P→◻Q)→◻(◻Q→◻P) (which is equivalent to ◊~(◻P→◻Q)→◻(◻Q→◻...
1
vote
1answer
105 views

Axiomatic proof of ⊢ □P → □◇□P in S4

As the title explains, I'm trying to give an axiomatic proof of ⊢ □P → □◇□P in S4. This is simple to prove in B, but I'm struggling to see how it's done in S4. I'd really appreciate any help you ...
1
vote
3answers
168 views

Modal validity & vagueness

(2nd version to make explicit my implicit assumptions about A, B and C, and the definitions of the non-logical constants "⊂" and "≡".) Intuitively, the following modal argument seems valid to me and ...
2
votes
2answers
173 views

Does ◻(∀x)(Fx ⊃ ◻(E!x & (E!x ⊃ Fx))) entail ◻((∃x)Fx ⊃ ◻(∃x)Fx)?

I was wondering if we can derive ◻((∃x)Fx ⊃ ◻(∃x)Fx) from ◻(∀x)(Fx ⊃ ◻(E!x & (E!x ⊃ Fx)))? (By the way 'E!' is the existence predicate.) I am using the Quantified Free Modal Logic constructed/...
3
votes
1answer
78 views

What is reflexivity in temporal logic?

According to Stanford Encyclopedia of Philosophy, reflexivity can be defined by : ∀x(x ≺ x) Where ≺ means "Precedes" : For all x, x precedes x But what does it mean for an instant in time x ...
2
votes
1answer
85 views

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 ...
0
votes
3answers
125 views

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?
1
vote
0answers
157 views

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) ∧ ...
0
votes
2answers
145 views

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 ...
2
votes
1answer
154 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” ...
0
votes
1answer
110 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 ...
2
votes
1answer
233 views

Is the problem of logical omniscience intractable?

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 ...
1
vote
1answer
82 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.)
2
votes
3answers
191 views

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 ...
3
votes
0answers
97 views

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? ...
2
votes
1answer
43 views

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-...
2
votes
1answer
60 views

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 ...
1
vote
1answer
135 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 ...
1
vote
1answer
276 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: ...