modal-logic

Extending propositional logic to modal logic in Haskell

由 有些话、适合烂在心里 提交于 2021-02-18 06:32:49
问题 I have written some code in Haskell for modeling propositional logic data Formula = Prop {propName :: String} | Neg Formula | Conj Formula Formula | Disj Formula Formula | Impl Formula Formula | BiImpl Formula Formula deriving (Eq,Ord) However, there is no natural way to extend this to Modal Logic, since the data type is closed. Therefore, I thought I should use classes instead. That way, I can easily add new language features in different modules later on. The problem is that I don't exactly

Interesting operators in Haskell that obey modal axioms

由 可紊 提交于 2019-12-10 01:59:00
问题 I was just looking at the type of map :: (a -> b) -> [a] -> [b] and just the shape of this function made me wonder whether we could see the list forming operator [ ] as obeying various axioms common to normal modal logics (e.g, T, S4, S5, B), since we seem to have at least the K-axiom of normal modal logics, with [(a -> b)] -> [a] -> [b] . This leads to my question: are there familiar, interesting operators or functors in Haskell which have the syntax of modal operators of a certain kind, and

Kripke semantics: learning software available?

由 扶醉桌前 提交于 2019-12-07 09:18:37
问题 I am stuck on Kripke semantics, and wonder if there is educational software through which I can test equivalence of statements etc, since Im starting to think its easier to learn by example (even if on abstract variables). I will use ☐A to write necessarily A ♢A for possibly A do ☐true, ☐false, ♢true, ♢false evaluate to values, if so what values or kinds of values from what set ({true, false} or perhaps {necessary,possibly})? [1] I think I read all Kripke models use the duality axiom : (☐A)->

Kripke semantics: learning software available?

由 女生的网名这么多〃 提交于 2019-12-05 16:42:45
I am stuck on Kripke semantics , and wonder if there is educational software through which I can test equivalence of statements etc, since Im starting to think its easier to learn by example (even if on abstract variables). I will use ☐A to write necessarily A ♢A for possibly A do ☐true, ☐false, ♢true, ♢false evaluate to values, if so what values or kinds of values from what set ({true, false} or perhaps {necessary,possibly})? [1] I think I read all Kripke models use the duality axiom : (☐A)->(¬♢¬A) i.e. if its necessary to paytax then its not allowed to not paytax (irrespective of wheither

Interesting operators in Haskell that obey modal axioms

由 时间秒杀一切 提交于 2019-12-05 01:30:35
I was just looking at the type of map :: (a -> b) -> [a] -> [b] and just the shape of this function made me wonder whether we could see the list forming operator [ ] as obeying various axioms common to normal modal logics (e.g, T, S4, S5, B), since we seem to have at least the K-axiom of normal modal logics, with [(a -> b)] -> [a] -> [b] . This leads to my question: are there familiar, interesting operators or functors in Haskell which have the syntax of modal operators of a certain kind, and which obey the axioms common to normal modal logics (i.e, K, T, S4, S5 and B)? This question can be
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