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devel / comp.lang.prolog / Re: conversion to conjunctive normal form

SubjectAuthor
* conversion to conjunctive normal formMark Tarver
+- Re: conversion to conjunctive normal formFred Mesnard
`- Re: conversion to conjunctive normal formMostowski Collapse

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conversion to conjunctive normal form

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Subject: conversion to conjunctive normal form
From: dr.mtarver@ukonline.co.uk (Mark Tarver)
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 by: Mark Tarver - Thu, 23 Mar 2023 20:22 UTC

Not specifically a Prolog problem but a logic problem,

Can anybody give me the CNF of this expression? You'll need a Prolog program to hand.

[[p <=> q] <=> r] <=> [p <=> [q <=> r]]

<=> meaning 'if and only if'; I don't care about the syntax too much. This is just check on a program I'm writing.

Mark

Re: conversion to conjunctive normal form

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Subject: Re: conversion to conjunctive normal form
From: frederic.mesnard@gmail.com (Fred Mesnard)
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 by: Fred Mesnard - Fri, 24 Mar 2023 11:14 UTC

The empty CNF because it's a tautology as logical equivalence is associative.

Fred

Re: conversion to conjunctive normal form

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Subject: Re: conversion to conjunctive normal form
From: bursejan@gmail.com (Mostowski Collapse)
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 by: Mostowski Collapse - Wed, 19 Apr 2023 17:18 UTC

Did you try LKF? Juggling with polarisation
might change the behaviour of such formulas.
You have at least two choices, a heuristic might

make a choice depending on polarity of context:

Choice 1:
A <=> B :<=> (A => B) & (B => A)
Choice 2:
A <=> B :<=> (A & B) | (~A & ~B)

See also:

Dale Miller: Focused proof systems
https://www.youtube.com/watch?v=u0iVN1_6nkc

Imogen: Focusing the Inverse Method
https://www.cs.cmu.edu/~fp/papers/lpar08.pdf

Mark Tarver schrieb am Donnerstag, 23. März 2023 um 21:22:08 UTC+1:
> Not specifically a Prolog problem but a logic problem,
>
> Can anybody give me the CNF of this expression? You'll need a Prolog program to hand.
>
> [[p <=> q] <=> r] <=> [p <=> [q <=> r]]
>
> <=> meaning 'if and only if'; I don't care about the syntax too much. This is just check on a program I'm writing.
>
> Mark

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