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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

Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality

388 questions
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What is modal logic for?

I understand "pure" logic as a structural description of what a valid proof is but I have never understood the reasons for using modal logic. What's an example typical of how modal logic is used?
user3085
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What are the practical applications of modal logic?

I'm a computer science and philosophy double major. I know logic is paramount in computer science, but what about modal logic? Are there any practical applications in computer science and perhaps even outside of computer science?
user14603
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How do I go from ◊∃x□[∃y(y=x) ∧ Mx] to ∃x□[∃y(y=x) ∧ Mx]?

I've been thinking about the ontological argument recently. I'm trying to go from ◊∃x□[∃y(y=x) ∧ Mx] to ∃x□[∃y(y=x) ∧ Mx] I choose that formulation because that seems to express x having the property of necessary existence and essential…
Dante Alighieri
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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 tomorrow, then it is possible that it will be sunny. But: what is…
Diploria
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How is Kripke-style modal logic distinct from classical propositional logic with additional axioms?

I've been considering the possible-worlds semantics for simple forms of modal logic, such as Kripke modal logic. This reading of modal logic seems to be a reduction to restricted truth-tables, where each row of the truth-table corresponds to the…
Niel de Beaudrap
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Is there a system of logic which denies DNI?

From what I know, the law of double negation is often simplified as p <=> ~~p. Intuitionist logic splits the biconditional into DNI and DNE. DNI: p -> ~~p DNE: ~~p -> p and denies DNE while affirming DNI. My question is whether there is a similar…
Kelvin Chan
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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 sphere of reality that can be perceived by each…
jimjim
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Modal Logic: a question concerning accessibility

I’m reading a lot about modal logic lately, right now Lewis “On the Plurality of Worlds” and Priests “Introduction to Non-classical Logics”. It is postulated that the different worlds have nothing to do with each other. Everything that belongs to…
Lukas
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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?
Beginner
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Is it possible to not know that one knows p?

An axiom that is often included in standard modal logic is Kp => KKp If we use epistemic modal logic, so that K translates as 'he knows', then recalling p stands for a proposition, we have that Kp translates as he knows proposition p so Kp =>…
Mozibur Ullah
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What's a good source for refreshing my formal logic skills prior to graduate school?

I need to flex my formal logic muscles prior to graduate school--I've had a dry spell in my logic practices while finishing my mathematics degree, particularly since the logic used in analysis, algebra, and topology is a pale shadow of my formal…
Asher
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Is there any relation beetwen justification logic and type theory?

Justification logics, was introduced by Sergei Artemov, are epistemic logics which allow knowledge and belief modalities to be ‘unfolded’ into justification terms: instead of □X one writes t:X, and reads it as “X is justified by reason t”.…
Ali
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How to Prove "Possibly P if Necessarily P" in Kripke Modal Logic?

I wish to prove the following within Kripke modal logic: □P → ◇P This is not a homework problem, but simply the first thing I'd like to prove. I've been able to prove more complex theorems such as □(P→Q)&◇P → ◇Q, but a straightforward proof of…
Chris Merck
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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 implies q, then if it is obligatory that p, then it is obligatory that…
David Gudeman
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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 universally which yields two interesting classes…
Avi C
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