Questions tagged [modal-logic]

Questions relating to deductions relating to the expressions "it is necessary that" and "it is possible that"

Modal logic is an extension of propositional and predicate logic that expresses modalities, which are qualifications to a statement. The most commonly used modalities in mathematics are "possibly," "necessary," and "impossibly."

For more information, see these links:

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100 blue-eyed islanders puzzle: 3 questions

I read the Blue Eyes puzzle here, and the solution which I find quite interesting. My questions: What is the quantified piece of information that the Guru provides that each person did not already have? Each person knows, from the beginning, no…
A Googler
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Gödel's ontological proof

Gödel's ontological proof is a formal argument for God's existence by the mathematician Kurt Gödel. Can someone please explain what are the symbols in the proof and elaborate about its flow: $$ \begin{array}{rl} \text{Ax. 1.} & \left\{P(\varphi)…
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Big Bang Theory Reference to Formal Logic

In the second episode "The Junior Professor Solution" of the 8th season of the Big Bang Theory, there exists a brief moment where Sheldon Cooper references one of his boards with what for a brief moment looked like a bunch of statements in some…
Doug Spoonwood
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What's the point of modal logic?

I was just reading about modal logic at wikipedia, and it seems that the usual approach is to introduce two new operations $\Diamond$ and $\square$ that mean 'possibly' and 'necessarily' respectively. I don't get this. If I wanted to say 'it is…
goblin GONE
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Understanding the modal necessitation rule

I understand that the modal necessitation rule is: $ \vdash p \Rightarrow \vdash \Box p $ That is, if p is a theorem then necessarily p is a theorem. But I don't quite understand what this means, or how I could use it in a modal proof. Obviously…
MDog
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Gödel's ontological proof and "modal collapses"

Recent findings on Gödel's ontological argument allowed to ultimately establish a couple of things: Gödel's original axiomata are inconsistent Scott's variation instead is consistent Scott's axioms imply the "modal collapse": every true statement…
Marco Disce
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What is the difference between intuitionistic, classical, modal and linear logic?

I am currently going through Philip Wadler's "Proposition as Types" and a passage of the introduction has struck me: Propositions as Types is a notion with breadth. It applies to a range of logics including propositional, predicate,…
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Common knowledge as a fixed point

I read on a wikipedia page that from the modal logic formalization CK can be formulated as a fixed point. If it also holds for the set theory formalization? If it does, where I can find about it? Edited: Common knowledge is used to be thought about…
Ilya
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Variants of Kuratowski's 14 set theorem

Kuratowski's 14 set theorem says that there are at most 14 sets one can obtain from a given set $A\subseteq X$ in a topological space $X$ by repeatedly applying the interior and complement operations. He also showed that if you add intersection to…
Andrew Bacon
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Books about modal logic?

I've just approached modal logic reading "An Introduction to Non-Classical Logic" of Graham Priest. I am looking for some books that treat this argument in a more extensive way than the book I am reading. I am especially interested in the…
Robbo
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The "set of all possible worlds", etc.

The following is an excerpt from a highly-respected paper (Angelica Kratzer, Modals and Conditionals: New and Revised Perspectives, chapter 1 "What Must and Can Must and Can Mean") (my emphasis): In the possible worlds semantics assumed here,…
kjo
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De re/dicto knowledge

Define $\mathcal{K}$ as a knowledge operator characterized by a S4 modal system. There is a distinction between de re and de dicto expressions of knowledge: $\exists x\mathcal{K}A(x)$ is a de re expression of knowledge: there exists $x$ such that…
Samuel
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Modal logic as a quotient Boolean-valued logic

I never really studied modal logic, but to my better understanding this is similar to classical logic adding two modal operations: $\square P\ $ meaning necessarily $P$, $\lozenge P\ $ meaning possibly $P$. Now if we consider Boolean-valued logic,…
Asaf Karagila
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Why is the Fixed-Point Axiom true?

In Epistemic Logic, the Fixed-Point Axiom says that $\varphi$ is common knowledge among the group $G$ if and only if all the members of $G$ know that $\varphi$ is true and is common knowledge: $$\vDash C_G\varphi \Leftrightarrow E_G(\varphi \land…
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Resources on finite Temporal Logic

I am looking for resources on finite Temporal Logic(s). I found some resources mentioning Past-Time TL, but I can't find any resource/paper describing it in any sort of detail and I was hoping that somebody here might be able to point me in the…
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