Questions tagged [modal-logic]
a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality
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Do things unknown automatically become unknowable in normal epistemic modal logic
Let's consider the following problem. I want to express in epistemic modal logic a statement that in some possible world some statement is unknown, but I don't want to express anything besides that. ...
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Proof of (Lp & Mq) -> M(p & q) within system K [closed]
I need a modal logic proof of (Lp & Mq) -> M(p & q) valid for system K. L is the necessity operator, M is the possibility operator, & is the conjunction operator, and -> is if/then.
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Propositional logic and modal logic
In propositional logic the following holds:
"(p and q) is true" iff "p is true" and "q is true"
In modal logic, the following commonly holds:
"(p and q) is ...
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Books on advanced formal and modal logic
I have read introduction books about formal and modal logic, and now I want to read more advanced ones. I have looked online yet didn't found one which matches my expectations. Does someone have one ...
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Can we meaningfully talk about "possibility" in a world without logical necessity?
Philosophers often distinguish between different types of modality—logical, metaphysical, physical, epistemic, etc. Logical possibility is usually treated as the broadest category: if something is ...
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Can Gödels ontological proof be parodied? [closed]
The original:
Ax.1: P(φ) ∧ □∀x (φ(x) → ψ(x)) → P(ψ)
Ax.2: P(¬φ) ⇔ ¬P(φ)
Def.1: G(x) ⇔ ∀φ [P(φ) → φ(x)]
Ax.3: P(G)
Thm.1: P(φ) → ◇∃x φ(x)
Thm.2: ◇∃x G(x)
Def.2: φ ess x ⇔ φ(x) ∧ ∀ψ [ψ(x) → □∀...
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Formal Consistency of a Logical Square with Randomness and Contingency [closed]
Defining a primitive modal operator 'Randomness' (R(P)) as ¬□P ∧ ¬□¬P creates logical equivalence with the standard operator for Contingency (◇P ∧ ◇¬P). Placing both R(P) and Contingency as distinct ...
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Is there a theory which is the true theory of logical reasoning?
Is there any theory of which any logician would be prepared to say that it is the true theory of logical reasoning?
If there is one, which is it, and who says that it is the true theory of logical ...
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Vacuous necessity vs. amodalism
Amodalism is the theory that some propositions lack modal profiles in the sense of being true, but neither contingently nor necessarily true. That is, modality is not usefully self-applicable: either ...
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Absentee and contrary formulas for hyperintensionality
Here's the SEP introduction of hyperintensionality in terms of operations:
If the concept is expressed by an operator, H, then H is hyperintensional insofar as HA and HB can differ in truth value in ...
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If there are set-theoretic multiverses of "possible" worlds, are there set-theoretic "impossible" worlds?
The SEP lists four main types of impossible worlds: impossible ways for worlds to be, general logic violators, classical logic violators, and contradiction realizers. I can easily see how the latter ...
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What do epistemologists like Williamson hope to achieve by going modal?
I've been reading Williamson's paper "Probability and Danger" and in it, he cites the following double bind when choosing between low-risk and no-risk theories of knowledge:
If we say that ...
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Axiomatic proof in modal propositional logic statement □(p→□p)→(◊p→□p) in system B
I am trying to prove the statement □(p→□p)→(◊p→□p) in system B of the modal propositional logic, but my trials failed.
The largest challenge I am facing is to prove ◊□p→□p in B-system. Obviously that ◊...
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If, "This sentence is demi-negated," doesn't make any sense, does that undermine the concept of demi-negation?
The inspiration for this question is an essay that starts with analysis of the "modal liar" sentence, to wit:
This sentence might not be true.
It seems possible to analyze said sentence ...
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If there are set-theoretic "possible worlds," are there set-theoretic "possible situations"?
The SEP entry on situations in natural-language semantics reads:
Situation semantics was developed as an alternative to possible worlds semantics. In situation semantics, linguistic expressions are ...
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