# 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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### What is modal logic for?

I understand "pure" logic as a structural description of what a valid proof is but I have never understood the reasons for using modal logic. What's an example typical of how modal logic is used?
2k views

### 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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### In modal logic, why not 'possibly p' → 'not necessarily p'?

I'm told that if ◇ means 'possible' and ◻ means 'necessary' and ~ means 'not' and ↔ means 'if and only if', then ◇P ↔ ~◻~P I get that if it is not necessarily not going to be sunny ...
1k views

### How do I go from ◊∃x□[∃y(y=x) ∧ Mx] to ∃x□[∃y(y=x) ∧ Mx]?

I've been thinking about the ontological argument recently. I'm trying to go from ◊∃x□[∃y(y=x) ∧ Mx] to ∃x□[∃y(y=x) ∧ Mx] I choose that formulation because that seems to express x having the ...
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### How is Kripke-style modal logic distinct from classical propositional logic with additional axioms?

I've been considering the possible-worlds semantics for simple forms of modal logic, such as Kripke modal logic. This reading of modal logic seems to be a reduction to restricted truth-tables, where ...
763 views

### 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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### 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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### 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, ...
927 views

### 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 □...
332 views

### Is it possible to not know that one knows p?

An axiom that is often included in standard modal logic is Kp => KKp If we use epistemic modal logic, so that K translates as 'he knows', then recalling p stands for a proposition, we have that Kp ...
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### Should truth entail possible truth?

It is a well-accepted axiom of modal logic that truth implies possible truth. Is there any philosophical argument against this conclusion? In other words, should truth entail possible truth?
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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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### What is the explanation for inferring existence in every possible world from existence in some in Plantinga's Ontological Argument?

I found the following version of the Ontological Argument online (I'm pretty certain its Plantinga's but I couldn't find an exact source). Here is how it goes: It is possible that a maximally great ...
633 views

### 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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### 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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### Nonexistence and invalid formulas in modal logic

In first-order logic, I can essentially just ignore issues related to nonexistence and invalid formulas, without losing much. There is also free logic, in case I'm not happy with simply ignoring these ...
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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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### 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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### Can logic be significantly geometrised?

Descarte has been lauded for putting together geometry and algebra, and his achievement allowed the invention of calculus by Leibniz & Newton and allowed its efficacious and explosive development ...
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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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### 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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### 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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### 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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### Is Modal Logic Logic?

What makes "Modal Logic" Logic? Why are symbols that stand for "necessary", for example, taken as symbols of Logic (of the same level of symbols that stand for "exists")? What are the limits that ...
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### Is there such a thing as provability of provability?

Gödel says that there are true statements that can't be proved, given a sound axiomatic system. Does anyone say anything about the provability of the provability of statements? Is it still an open ...
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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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### Classical possible worlds semantics

It looks like to me that possible worlds semantics are closely associated with propositional modal logic (or interior/closure algebras). Is there any literature where possible worlds semantics is ...
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### What are the prerequisites for studying modal logic?

A book I'm currently reading briefly mentioned epistemic logic, but didn't say what it was. Since I've never heard of this logic I decided to look it up and saw that it was a type of modal logic. I ...
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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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### Does modal realism dispense with Occams razor or embodies it?

Modal realism posits the reality of all logically possible worlds. This seems to radically dispense with Occams razor by allowing the reality of all logically feasible explanations. But on reflection ...
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### Does semantic externalism imply modal realism?

Semantic externalism, or more broadly externalism about mental content, is the idea that propositions, intentions, attitudes, etc. derive their meaning from the external world as opposed to internally ...
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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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### Establishing Incompletenes of Modal LPC

In Hughes and Cresswell A New Introduction to Modal Logic (1996 ed.) page 271, they attempt to establish the incompleteness of the system K + G1 + BF (where K is L(P->Q)->(LP->LQ), G1 is MLP->LMP, and ...
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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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### Is knowledge really related to propositional modal logic?

Browsing on the Internet, it seems to me that knowledge (viz. the ability to know that) is invariably linked to propositional modal logic. Why is that? Could we not say, for instance, that knowledge ...
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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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### 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 ...
153 views

### 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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### 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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### 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 ...
516 views

### What's the difference between being spatiotemporally isolated and causally isolated?

In this Wikipedia article on modal realism, section "Main tenets of modal realism", there's a list of six tenets. Here are the fifth and the sixth of them: 5.Possible worlds are unified by the ...
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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 ...
821 views

### 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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### Logic Notation Question: [[A]] vs. ⌈A⌉

Let A stand for an arbitrary proposition. I've read some papers recently that use differing notation on expressing the notion that "A is true". The two I'm concerned about are as follows: (1) [[A]...
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### Does S4 (and B) hold for the strongest interpretations of ♢ and □?

Suppose these are the interpretations we are working with: ♢Ψ iff no explicit contradiction can be deduced from Ψ in FOL or in other words it's not provable that ~Ψ in FOL. ~♢Ψ iff an explicit ...
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### What is the difference between 'instantiate' and 'exemplify', if any?

In this lecture series, Stalnaker uses both verbs 'instantiate' and 'exemplify'. Now, I gather those two verbs have the same meaning. But, I also think that if the two verbs were equivalent, Stalnaker ...
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### What are good sources on vivid designators?

Wikipedia lists a vivid designator as the following: Vivid designator: In modal logic and the philosophy of language, a vivid designator is a term which is believed to designate the same ...
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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 ...