Questions tagged [modal-logic]

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Modal logic S4 system

How to prove in S4 system modal logic that ◇□◇x->◇x? Probably i only need to show that ◇□x->x Any help will be great?
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Why we can't use deduction theorem on soundness to contravene second incompleteness with lob's theorem

I'm starting to learn modal logic and there is something that's bothering my mind for a while. we know from deduction theorem that $((\vdash q) \rightarrow (\vdash p)) \Leftrightarrow(\vdash (q \...
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CTL trouble translating text into formula

I have an excercise where I have to translate verbally formulated statements into CTL formulas. I have particularly trouble with this one: On every path q is true at least once and p was true ...
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Uses of of the one-variable fragment of first-order logic aka S5

I'm looking at decidable fragments of first-order logic. It seems that FO(1), i.e. the one-variable fragment of first-order logic is equivalent to the modal logic S5. However, I cannot find a ...
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How to understand quantifier without predication " ∀(λφ. (φ x m→ φ y))"?

I am reading about embedding/automation of modal logics in classical higher order logic (http://page.mi.fu-berlin.de/cbenzmueller/papers/C46.pdf) and Goedels proof of God's existence is prominent ...
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$(\Box \forall x \varphi) \to (\forall x \Box \varphi)$?

I am working with a particularly forgiving interpretation of $\Box$ in Modal Predicate Logic. $M, w, g \models \Box \varphi$ iff for every $w' \in W$ such that $wRw'$, $M, w', g \models \varphi$ IF $\...
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4 votes
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Euclidean Models

I am asked to prove that every Euclidean models satisfies $\diamond \diamond \diamond \varphi \to \diamond \diamond \varphi$. How can this be done? I don't see how it could even be true.
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Meaning of the "why not" modality from linear type theory?

In linear type theory there is a modality written ! where !T can be read as "infinite copies of ...
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Is it possible to define logic programming for every logic that has implication and conjunction connectives?

Is it possible to define logic programming for every logic that has implication and conjunction connectives? Does logic programming adds something new to the usual inference process. By usual ...
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How to translate lambda calculus into (first-order, modal) logic, is it possible at all?

It is possible (using formal semantics) to translate natural language sentences into lambda expressions. So, is it possible to translate those lambda expressions into some logic, e.g. into first-order ...
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How to express modalities in lambda calculus - are some extensions required?

Lambda calculus can be used for encoding semantics of natural language, e.g. http://yoavartzi.com/tutorial/ contains full details about semantic parsing of natural language: converting natural ...
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How to express modalities in rule bases, knowledge bases or expert systems?

Knowledge bases and expert systems are usually production rules systems and as such they lack expressive means for expressing modalities like "agent believes in statement", "agent has duty to perform ...
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How to represent software code for code generation / automatic programming? How to integrate procedural and declarative knowledge?

I am learning about deontic logics and there I can make the following inferences: If A then there is **duty to create an entity of class C**, ...
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Modal Logic - □ distribution over →

In the modal logic K does □ distribution over →? For example, would the following be correct? □(p → q) ≡ □p → □q
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Kripke Models - evaluating the meaning of $\Box\Box p$

In Kripke models the evaluation of $x \vdash \Box p$ would be that every world reachable from $x$ satisfies $p$. But how would the truth of $\Box\Box p$ be evaluated in Kripke models?
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Modal logic axiom S4, transitive and reflexive frame, tableaux solver

I have a difficult problem to solve which as mentioned in the title is related to modal logic axiom S4. So, here is some background knowledge that can be useful: S4 axiom is a class of transitive and ...
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complexity of modal logic axioms

I am writing a paper in which I want to include complexity results for different modal logics and possibly add a reference to a specific paper. At the moment I have the following: K- no restrictions ...
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The use of modal logic in computer science [closed]

I have a tentative understanding of modal logic. Can anyone explain modal logic as it is used in computer science?
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Intuitive meaning of modal $\mu$-calculus formula

I am solving one of the past exams and I am not certain with my solution to one of the exercises. The exercise is asking to give intuitive meaning to modal $\mu$-calculus formula: $$ \phi = \mu Z. \...
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3 votes
3 answers
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Why is GFp -> GFq false in LTL, even though GFp and GFq are false?

Consider the Kripke structure: $$ \begin{array}{ccccccc} \to & (p, \neg q) & \to & (\neg p, \neg q) & \to & (\neg p, q) \\ & \circlearrowright & & \circlearrowright ...
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