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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Is there modal logic without possible worlds?
Would it be desirable to carry out a deflationary research programme in modal logic? In other words, would it be desirable to re-think modal logic without the possible worlds semantics? The original ...
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How does Plantinga's free will defense of God's benevolence work?
The purpose of the defense is to show that omniscient, omnipotent and benevolent God is consistent with the existence of evil in creation. The most popular version of the defense is due to Alvin ...
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What do necessity and possibility mean in Aquinas' Third Way argument for the existence of God?
In his famous Summa Theologica, the Scholastic theologian Thomas Aquinas presents Five Ways to demonstrate the existence of God. Here is Aquinas' Third Way, the argument from contigency:
The third ...
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How does the concept of the 'virtual' (Deleuze) relate to 'counterfactuals' (Lewis)?
We read:
"[...] Deleuze will reject the notion of the possible in favor of that of the virtual. Rather than awaiting realization, the virtual is fully real; what happens in genesis is that the ...
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Has any philosopher ever claimed that possibility can't really be tensed?
Has any philosopher ever claimed that possibility can't really be tensed? So that whatever will be possible is possible now.
I really have no idea, and would love an answer. I'll add my motive, so ...
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Is the problem of logical omniscience intractable?
Vincent Hendricks and John Symons notes the following about epistemic logic:
Epistemic logic gets its start with the recognition that expressions like ‘knows that’ or ‘believes that’ have systematic ...
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What are the practical applications of modal logic?
I'm a computer science and philosophy double major. I know logic is paramount in computer science, but what about modal logic? Are there any practical applications in computer science and perhaps even ...
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How can a tautology not be necessarily true?
My logic/philosophy exercises include the following statement:
"Every tautology is knowable a priori but not every tautology is necessarily true."
I'm bamboozled. How can a tautology not be ...
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Can truths about the natural numbers vary across possible worlds?
The truths of logic are the same in all possible worlds. However, what about truths about natural numbers? Like, for instance, is there a world where there are only finitely many primes, or a world ...
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Is there a name for each individual's perceived sphere of reality?
Is it an acceptable idea that each individual carries their own model of reality in their mind?
Is there a name for the model that each individual uses to perceive reality? Is there a name for the ...
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How to Prove "Possibly P if Necessarily P" in Kripke Modal Logic?
I wish to prove the following within Kripke modal logic:
□P → ◇P
This is not a homework problem, but simply the first thing I'd like to prove. I've been able to prove more complex theorems such as □...
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Modal Logic: a question concerning accessibility
I’m reading a lot about modal logic lately, right now Lewis “On the Plurality of Worlds” and Priests “Introduction to Non-classical Logics”.
It is postulated that the different worlds have nothing to ...
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Are there mathematical properties a mathematical object might have only contingently?
It is generally assumed that mathematics is necessary, such that any mathematical theorem is necessarily true. This can be read as a de dicto necessity such that for any mathematical proposition p, []...
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Are there any established logical symbols for merely possible and contingently true?
In modal logic we have:
P → ◇P - If something is true, then it is true at some possible world.
◻P → P - If something is necessarily true, then it is true.
However, the reversed conditionals don't hold ...
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What determines accessibility of possible worlds?
Recently, I have begun studying modal logic, using Brian Chellas's Modal Logic: An Introduction. Something keeping me from fully understanding the material is the idea of a possible world. They seem ...
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Why substitutivity doesn't work in an intensional context?
I was trying to grasp some more insights on the difference between intensional and extensional.
I started reading this article by Melvin Fitting on intensional logic. It seems interesting but I ...
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General sentence operators
There are lots of operators that act on sentences. Here are a few examples:
P and Q
not P
forall x.P
necessarily P
eventually P
x believes that that P
it is obligatory that P
etc. The first two ...
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Why is Hesperus necessarily Phosphorus?
"Hesperus (the evening star) is Phosphorus (the morning star)" is one of Kripke's examples of necessary aposteriori, statements that are true necessarily if true at all, even if their truth can only ...
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Can possible-but-non-actual objects have accidental properties?
The modal logic I am considering is the "Simplest Quantified Modal Logic" which combines first-order predicate logic with identity, with S5 in the most straightforward way, described here and slightly ...
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What is Quine's perspective on probability?
I am curious about what Quine's perspective on probability may be and if we can say that the quinean viewpoint on modality can be considered similar to his viewpoint on probability.
Is probability ...
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Does anyone have a proof checker they prefer using for modal logic?
I am looking for a proof checker for modal logic using natural deduction or sequent calculus.
I am trying to learn Isabelle, but I think there should be a simpler solution.
Although I can rely on ...
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Identity in Quantified Modal Logic
Why is ¬(◇(a=b)∧◇¬(a=b)) a validity in Quantified Modal Logic (QML)? For example, let a:=“the present King of France” and b:=“the richest bald person alive”. Then, it seems ◇(a=b)∧◇¬(a=b) is not a ...
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Rigid designators, equality and functions in many-valued logic and (simple) quantified modal logic [closed]
After reading "In Defense of the Simplest Quantified Modal Logic", I wonder how to add functions to the language of the simplest quantified modal logic (QML for short). The simplest model of QML has a ...
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Does the finitary proof of the consistency of relevant PA shows that first order PA is irrelevant?
Relevance logic takes a closer look at the implication operation in first-order logic. It suggests that implications such as:
p and not p -> q
cannot hold; in ordinary English, an example of this ...
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Many-worlds interpretation of QM and modal realism
Does the difficulty of making sense of quantum mechanical phenomena, (i.e. arriving at a nice philosophical interpretation of QM) taken together with Everett's many-worlds interpretation, constitute ...
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What are the objections to the axioms of modal logic?
I am looking for good/classical references on objections/criticism of modal logic.
I am a bit familiar with the work of Quine but find his objections around the paradoxes of material implication or ...
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What exactly is metaphysical possibility?
In the literature about the epistemology of modality I stumbled upon various types of possibilities, e.g. epistemic possibility, metaphysical possibility. I have a rough unterstanding of these, but ...
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Who Invented the Modal Fallacy?
The Modal Fallacy is the best known of the fallacies related to Modal Logic. But, it is difficult to find the name of the logician who established the modal fallacy. Was it Aristotle? And, how does ...
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Is there anyone who believes that all modal statements are meaningless or trivial?
It is often useful to interpret statements in various modal logics using possible-world semantics. For instance "it is necessary that P" means "P is true in all possible worlds", "it is possible that ...
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Is it provable that epistemically possible (possible for all I know) does not imply possible?
Here is an argument that it is not. Let's start with some equivalences:
X is epistemically possible
iff
X is possible for all I know
iff
not (X is impossible given what I know)
iff
X is not ...
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Why did many valued logic fail in describing modal logic?
The SEP article on many valued logic makes the following statement:
The introduction of systems of MVL by Łukasiewicz (1920) was initially guided by the (finally unsuccessful) idea of ...
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What is the difference between ∃ (existence) and A (actuality)?
The existential quantification can, it seems, be used with modal logic. Now excuse my naivety, but:
if so, what is the difference between being actual and existential quantification?
I'm just asking ...
user6917
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Are the truths of euclidean plane geometry contingent truths?
Existence of non-euclidean geometries does not seem to imply an affirmative answer to that question. It might be possible that such geometries are formal constructs to abstract our primitive and ...
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On that p does not imply necessarily p
Am I right to assume that in no modal logic, whether in K or in a logic where the accessibility relation is specified as either reflexive, symmetrical or transitive, does ”p implies necessarily p” ...
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What is the fallacy in deriving necessity of an event from God's foreknowledge of it?
Here is the form:
If God knows I will eat lentils tonight, then necessarily I will eat lentils tonight
God knows I will eat lentils tonight
Therefore, necessarily I will eat lentils tonight.
Now, ...
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Prove ◇(p ∨ q) → (◇p ∨ ◇q) and ◇(p ∧ q) → (◇p ∧ ◇q) in Modal Logic K
I would really appreciate a rundown of a proof of one of the formulas or both:
1) ◇(p ∨ q) → (◇p ∨ ◇q)
2) ◇(p ∧ q) → (◇p ∧ ◇q)
I'm allowed to use following proof procedures of modal logic K:
1) ...
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Does ◻(∀x)(Fx ⊃ ◻(E!x & (E!x ⊃ Fx))) entail ◻((∃x)Fx ⊃ ◻(∃x)Fx)?
I was wondering if we can derive ◻((∃x)Fx ⊃ ◻(∃x)Fx) from ◻(∀x)(Fx ⊃ ◻(E!x & (E!x ⊃ Fx)))? (By the way 'E!' is the existence predicate.)
I am using the Quantified Free Modal Logic constructed/...
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Modal Logic: A Clarification
This is presumably an extremely basic question, but I didn't have any luck on my preliminary attempts to Google an answer or track one down here.
After hearing a number of debates and presentations in ...
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How can you derive De Morgan's Law?
Can someone help me prove De Morgan's Law. In my logic class we are using a very basic set of rules for derivations and I can't for the life of me figure out how to prove the law with them. It's not ...
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Can a valid argument with formally consistent premises have an analytically impossible conclusion? What about the converse?
Can a valid argument with formally consistent premises have an analytically impossible conclusion? What about the converse; analytically compossible premises, but a conclusion that is a formal ...
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Semantic expressiveness of modal logic
I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself:
P1 ◇ ∀a, ∃x // GNB(x, a) ∧ C(a)...
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Does the forcing phenomenon prove some sort of set-theoretic multiverse?
It seems that, "A can be forced to equal B," allows, "A is possibly equal to B." In possible-worlds lingo, this gets us, "There is a possible world where A = B." Since ...
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What is the counterexample in modal system K for "⬜A ➡A"?
As I understand it from Modal Logic 2.1 - the systems M, B, S4 & S5, I should not be able to show "⬜A ➡A" in modal logic K. The following truth tree seems to confirm this, if I did it correctly:
...
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Justification for axiom OB-RE in deontic logic
Let OB p denote "p is obligatory". Axiom OB-RE is (p ↔ q) → (OB p ↔ OB q). This axiom seems false to me (under the interpretation of obligation). For example, let p denote "don't lie to me" and q ...
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Quantified Logic and Unquantified Modal Logic
Is there a need to study unquantified modal logic if one knows the quantified PC logic very well? There seems to be an obvious connection between Possibility and the Existential Quantifier, and ...
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Necessity in relation to possibility
(1) Does necessity (materially) imply possibility?
(2) Does possibility (materially) imply necessity?
From a logical point of view:
If by material implication (A -> B), we mean (-A or B), then it ...
user13738
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Requesting help with designing curriculum (Logic)
I am currently a math major in university who wants to design my own area of study/major, specifically in Logic. I was wondering if I could get some help on how Logic sets itself apart from philosophy?...
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How to prove ◻(ϕ → ψ) → (♢ϕ → ♢ψ) a theorem of the normal modal logic S5? [closed]
I feel like this is the inversion of logic 5, so my intuition is that we cannot prove it a theorem of logic 5... But I am not sure at all
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