# 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

200 questions
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### Is the Counterfactual Conditional Closed Under Entailment?

I often read that the counterfactual conditional "is standardly held to be closed under entailment", but I am not sure if I understand what it means: Say p counterfactually implies q, and q implies r; ...
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### Modal Realism: Possible Worlds spatio-temporally isolated?

In Lewis' 5th doctrine of possible worlds in modal realism it says: Possible worlds are unified by the spatiotemporal interrelations of their parts; possible worlds are spatiotemporally isolated from ...
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### Conditional logic - how to apply a conditional with complex antecedent in tableaux?

I'm referring to the conditional logic of C+ as described Graham Priest in "An introduction to non-classical logic" chapter 5, where the strict conditional is enhanced with ceteris paribus, and a ...
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### What is the difference between a probability and a possibility?

I ask this in a fairly naive way. I understand that "probabilities" can be quantified in frequencies, degrees of belief, etc. with some defined "space" of probability.But I know little about modal ...
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### Question on the duality between necessity/knowledge and possibility [closed]

(1) Who first said that necessity and possibility are dual to each other? (2) Who first said that knowledge and possibility are dual to each other?
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### Intrinsically versus necessarily [closed]

The weakest normal modal logic, named K in honor of Saul Kripke, is simply the propositional calculus augmented by □, the rule N, and the axiom K. K is weak in that it fails to determine whether a ...
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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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### Does Aristotle recognize the Modal scope fallacy in his rejection of the sea battle argument?

Modal fallacy deals with modal logic, a 20th century construct, as user @Virmaior comments in his comment to the question Who Invented the Modal Fallacy?. However, in discussing the sea battle ...
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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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### Is an impossible proposition necessarily false

In modal logic, if one knows a proposition p, then p is true (though the converse does not necessarily hold). Suppose now that p is impossible. Does that mean that p is false (though a false ...
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### Modal Logic Question [closed]

I am currently reading a paper and the following statement is used: Fact "A" for individual i happens if and only if condition B is fulfilled for i possibly not, though not necessarily exclusive of, ...
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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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### Indiscernibility of possible worlds

According to Lewis, possible words are indiscernible from each other, that is, an individual in a possible world cannot say in which world it resides. It's somewhat similar to the indiscernibility of ...
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### What is the connection between temporal and epistemic knowledge?

Recently I read all kinds of work from logic scientists in which epistemic logic was the main topic. Where epistmic change refers to change in knowledge of some agent in a multi-agent system (in a non-...
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### Interpretation of implication symbol in modal logic

Suppose we have two propositions p and q, and an implication of this form: p → □q I can think of two potential interpretations of the meaning of this in terms of possible worlds: If p is true in ...
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### Modal Logic Proof, a formula is valid just if relations have a property

So I'm trying to prove that, in a language with two diamonds <1>,<2>, the formula p -> [2]<1> p is valid just in case for any x,y and R2(x,y) then R1(y,x). I have the "if" direction easily, ...
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### Introduction Modal Logic with emphasis on metaphysics - free will particularly - and also mathematical logic

I'm reading Timothy O'Connor's 'Persons & Causes The metaphysics of free will' and the first chapter briefly goes into (though without introduction) the application of modal logic and ...
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### Ontology: How do ideas exist?

There are several ways of looking at ideas. There is a platonic way of looking at ideas which sees the ideas as kind eternal entities. Augustine puts these ideas in the mind of God. In either case ...
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### What's a good source for refreshing my formal logic skills prior to graduate school?

I need to flex my formal logic muscles prior to graduate school--I've had a dry spell in my logic practices while finishing my mathematics degree, particularly since the logic used in analysis, ...
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### Questions from a new introduction to modal logic by Hughes and Cresswell

I just want to see if I got this correct. Show that the following wff is valid in every seating arrangement: Mp -> (Lq->Mq). Here's my argument: Assume player A sees at least one player B that ...
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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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### Why is most modal logic about necessity vs possibility rather than permission or wishes?

It seems to me that the notions of modal logic are all shaped primarily by one modal, 'can/must' (konnen/mussen). Has anyone looked at all deeply at how this convention compares with the other common ...
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### Please explain this paragraph of van Inwagen (First Argument for Incompatibilism)

In An Essay on Free Will, van Inwagen tries to define his notion of the laws of nature (for his First Argument that follow), this is the concluding paragraph: Thus, on our "sets of possible worlds" ...
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### Need Help Fully Understanding the Claim: Every normal modal logic, L, is an extension of K

I am clear on everything that precedes the grey box. I just can't wrap my mind on how we can possibly get more valid inferences from a proper subset of interpretations than we could from the original ...
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### Suppose you know the premises of an argument are inconsistent. Do you have to do a truth table to know whether it is valid or invalid?

Suppose you know the premises of an argument are inconsistent. Do you have to do a truth table to know whether it is valid or invalid?
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### Suppose the conclusion of an argument is known to be tautologous. Do you have to do a truth table to know whether it is valid or invalid?

Suppose the conclusion of an argument is known to be tautologous. Do you have to do a truth table to know whether it is valid or invalid?
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### Suppose the conclusion of an argument is logically equivalent to the conjunction of all the argument’s premises

Suppose the conclusion of an argument is logically equivalent to the conjunction of all the argument’s premises (the conjunction of all the arguments premises is just the statement obtained by taking ...
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### Existential priority and modality

Since existence is logically or conceptually prior to necessity, it would seem that "necessary existence" is an incoherent assertion. Therefore, what is the status of "necessity" as a modal claim? ...
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### Formal Modal Logic and Metaphysics

I have been reading some introductory metaphysics (Van Inwagen's book of the same name) and I encounter arguments using modal logic. I am unsure how to interpret these - the arguments (chapter 6 and 7)...
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### Is there an intrinsic hidden modal logic within ordinary Boolean algebras?

Is there an intrinsic, hidden modal logic within ordinary (abstract) Boolean algebras? I do not question whether interior or closure algebras are Boolean algebras. Nor do I seek for an explanation of ...
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### How does negation operate in modal logic?

I was mulling over this proposition: Just because something is provable doesn't mean that it is important; and wanted to consider its contrapositive. How would I write this in formal (modal) logic? ...
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### Does Flatland exist according to modal realism?

Does Flatland exist according to modal realism, since it is a possible world?
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### How to show non consequence / logical consistency?

How would I show non-consequence with this set? I can't seem to figure out the significance of the Universal and Existential indicators here. (∀x)(∃y)Fxy (∃y)(∀x)Fxy and the other question i'm ...
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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 dual of a modal operator in justification logic work?

In justification logic, given a formula A, one can have modal formulas of the form 't : A', read as 't justifies A' or 't is evidence for A'. Has there been any investigation of what the dual of such ...
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### Assuming P means the same as Q and Bob believes P and is aware that P means the same as Q, can we conclude he believes Q?

Assuming Bob is a fairly rational person. If this is not the case, then is there a way to modify it? Also, is this the argument that Frege is making in "On Sense and Reference" that "the morning star" ...
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### What is the fallacy? “I never lost in tennis against Roger Federer.”

Example I never lost in tennis against Roger Federer. It's a negation and 'true' but it's misleading. In fact I never played tennis against Federer. I'm looking for a name or a category for these ...
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### Why is it wrong to deduce determinism from a logical law?

In Aristotle's famous sea battle argument, he argues from bivalence (or something like it) to determinism. Stalnacker has an argument to determinism using standard logical laws, as well. My question ...
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### Can deontic conditionals be indicative? [closed]

To check my understanding, the following is an indicative deontic conditional, correct? "If you live in Texas, you ought to watch football." It is indicative in the sense that it is reporting on a ...
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### What are the ways one can use to demonstrate that it's possible for something to exist?

Notice that I'm not talking here about the actual existence of something, but the possibility of existence. About such ways, I only know one that is argumentative (which is the kind I would like to ...
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### What kind of conditional does Nozick use in his theory of knowledge?

Knowledge is traditionally defined as justified true belief: in order for S to know P, S must believe P, P must be true, and S must be justified in believing P. Now this definition has been ...
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### How does 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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### Non-modal approach to necessity and possibility

Is there such thing that a non-modal approach to necessity and possibility? I read on Wikipedia (see David Lewis's page, introductory paragraph) than Lewis's Modal Realism can provide such an ...
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### Is there any relation beetwen justification logic and type theory?

Justification logics, was introduced by Sergei Artemov, are epistemic logics which allow knowledge and belief modalities to be ‘unfolded’ into justification terms: instead of □X one writes t:X, and ...
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### What if what is possible follows from logic alone

Suppose that every imaginative variation [I don't mean this in any technical sense] of what is physically possible is necessarily possible: because what I can imagine follows from logic alone. ...
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### If modality across some domain was such that anything is possible, then does modal logic entail that everything actual is necessary?

If modality across some domain was such that anything is possible, then does modal logic entail that everything actual is necessary? It seems intuitive that would be the case.
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### What does w ∈ V(p) mean?

I have been recently looking at the Handbook of Modal Logic and have come across the following definition: M, w ⊨ p iff w ∈ V(p) I dont understand how w could be an element of V(p) where V assigns a ...
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### Proof of the reflexivity of the accessibility relation

If accessibility is defined as follows: Definition 1. wRw' ↔ ∀p (w' ⊨ p → w ⊨ ◊p) and the following axioms hold: Axiom 1. p → ◊p, Axiom 2. ∀p∀w (w ⊨ p → w ⊨ ◊p), are ...