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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

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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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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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Nonexistence and invalid formulas in modal logic

In first-order logic, I can essentially just ignore issues related to nonexistence and invalid formulas, without losing much. There is also free logic, in case I'm not happy with simply ignoring these issues. While trying to make sense of a…
Thomas Klimpel
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What determines accessibility of possible worlds?

Recently, I have begun studying modal logic, using Brian Chellas's Modal Logic: An Introduction. Something keeping me from fully understanding the material is the idea of a possible world. They seem to be described as maximally-consistent sets of…
ElStevo
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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: Necessity introduction: if you have a strict…
Matt Dickau
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Need Help Fully Understanding the Claim: Every normal modal logic, L, is an extension of K

I am clear on everything that precedes the grey box. I just can't wrap my mind on how we can possibly get more valid inferences from a proper subset of interpretations than we could from the original set of interpretations. Can anyone explain this…
Acemanhattan
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Is every world accessible to itself?

I just realized that for the proposition "If p is necessarily true then p is true", i.e. "box p implies p", to be a tautology, we need the condition that every world is accessible to itself. That is, for every model M=(W,R) we need the reflexivity…
Janitha357
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Why did many valued logic fail in describing modal logic?

The SEP article on many valued logic makes the following statement: The introduction of systems of MVL by Łukasiewicz (1920) was initially guided by the (finally unsuccessful) idea of understanding the notion of possibility, i.e. modal logic, in a…
Alexander S King
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Understanding possible world semantics and time

In possible world semantics, statements of the form "It is possible that P" are interpreted as meaning "There is some 'possible world' in which P is true". And if you're a modal realist, then these possible worlds are other universes in the…
Benjamin Grange
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Are there modal operators that don't take a proposition as an argument?

All of the modal propositions I can think of are most reasonably analyzed as a modal operator applied to a proposition, and possibly other arguments. In the following examples, I'll write the arguments to the modal argument in parentheses: It is…
David Gudeman
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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” hold? In what (if any) ways does the accessibility…
simulacra
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The converse to the C modal logic axiom - has it been studied?

There is a C axiom as mentioned at https://plato.stanford.edu/entries/logic-modal/#MapRelBetModLog in Section 8. My question is: what can be said about the formula which is the converse of the C axiom? I have been trying to find out whether the…
Monica
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What does w ∈ V(p) mean?

I have been recently looking at the Handbook of Modal Logic and have come across the following definition: M, w ⊨ p iff w ∈ V(p) I dont understand how w could be an element of V(p) where V assigns a truth value to p. So in other words, what does 'w…
user8083
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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 of "merely necessary" things (things necessary…
Kristian Berry
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