# 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?
1 vote
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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.
137 views

### 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 ...
122 views

### 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 ...
136 views

### 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 ...
215 views

### 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**, ...
113 views

### 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?
446 views

### 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 ...
130 views

### 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 ...