Questions tagged [modal-logic]
21 questions
6
votes
1 answer
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?
Älskar
- 264
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5
votes
2 answers
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 T".
According to ncatlab, there is a dual to this modality which is sometimes written ?T and referred to as the "why not" modality. What is the meaning…
Andrew Cann
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4
votes
1 answer
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 language texts into lambda expressions - Cornell…
TomR
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4
votes
1 answer
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 reference (everybody references a German article of 1933…
Nicola Gigante
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4
votes
2 answers
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.
Logos
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3
votes
0 answers
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 logic or into modal logic?
I am aware of the…
TomR
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3
votes
0 answers
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 action", "agent has permission to perform…
TomR
- 1,411
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3
votes
1 answer
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 reflexive frames
S4 satisfiability problem is…
marcincuber
- 137
- 5
3
votes
1 answer
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 on the frame, NPComplete
T- reflexive,…
user45985
- 31
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3
votes
3 answers
Why is GFp -> GFq false in LTL, even though GFp and GFq are false?
Consider the Kripke structure:
$$
\begin{array}{ccccccc}
\to & (p, \neg q) & \to & (\neg p, \neg q) & \to & (\neg p, q) \\
& \circlearrowright & & \circlearrowright & & \circlearrowright & \\
\end{array}
$$
where $(p, \neg q)$ means “$p$ and not…
dendini
- 31
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3
votes
1 answer
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 sometime before, after
no longer.
My attempt is the…
Iwan5050
- 135
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3
votes
1 answer
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 example here…
TomR
- 1,411
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3
votes
0 answers
$(\Box \forall x \varphi) \to (\forall x \Box \varphi)$?
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 $\varphi$ is defined in $w'$. This mostly means…
Logos
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2
votes
0 answers
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 inference process I mean the construction of the…
TomR
- 1,411
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2
votes
1 answer
Modal Logic - □ distribution over →
In the modal logic K does □ distribution over →?
For example, would the following be correct?
□(p → q) ≡ □p → □q
Älskar
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