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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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.
user6917
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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 the following claims true?
...
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Logical Form of an Appeal to Probability
How can you express an "Appeal to Probability" argument in a logical notation? Feel free to use any forms or renditions of logic, including APL, as I know there are different symbols that can be used. ...
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Help with a modal Hilbert-style proof of (□(a>b)&◊(a&c))>◊(b&c)
Can't grasp how it can be proved. To proof just propositional calculus formula (without modal operators) at first seems rather natural to me. Tried the law of importation scheme but it didn't work out....
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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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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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What is the Difference between Vagueness and Indeterminacy?
Is "There will be a sea battle tomorrow" a borderline case of vagueness? Or, is it a case of modal indeterminacy? Or both? Where do we draw the line between the two? And ,what about "There is a sea ...
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Classical and Medieval Scholars on Modal Logic
Who most influenced the development of modal logic prior to the nineteenth century - aside from the Aristoteleans, Dialecticals, and Stoics of course?
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Does necessary possibility entail actuality?
In Modal logic,
Does being necessarily possible entail actuality?
user6917
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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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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 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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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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Is Deontic Logic applicable in Computer Science?
Deontic logic gives rise to a number of paradoxes when applied to our reasoning about moral values. These days it is starting to be applied in computer science. My worry is: doesn't the presence of ...
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Provide an example of two sentences , the first formally implying the second, the second analytically(but not formally) implying the first
Provide an example of two sentences , the first formally implying the second, the second analytically(but not formally) implying the first. Are two such sentences formally equivalent? Are they ...
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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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What is this special, general type of atomic sentence?
There is exactly one atomic sentence form of L (call it 'A'), which is always a tautology, and whose negation 'negate A', is always a formal contradiction. What is this special, general type of atomic ...
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Are the following relations reflexive/irreflexive/neither? Symmetric/asymmetric/neither? Transitive/intransitive/neither?
Are the following relations reflexive/irreflexive/neither? Symmetric/asymmetric/neither? Transitive/intransitive/neither?
1) x is a biological father of y
2) x is between point a and y. (Here, let ...
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Which of the following sentential operators are truth functional ? Why?
Which of the following sentential operators are truth functional ? Why?
1) '___ 'formally implies '__' in L.
2) '_____' analytically implies '__' in L.
3) Were it not true that '__', then '_' L.
4)...
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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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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 ...
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In modal logic what is the difference between M,w |= p and M | q, w |= p?
Where p designates some proposition, M designates a model and w designates a world. Sorry if this question is too basic, but I think it is so basic that none of the basic textbooks and articles which ...
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Nomologically possible worlds and physicalism
As I understand, nomologically possible world is a world which is governed by the laws of physics of the actual world, but doesn't that kind of entail that in all nomologically possible worlds (...
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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 ...
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Can three valued logic serve as an adequate basis for a (nontraditional) modal logic?
I asked a similar question on the Math Stack Exchange, but the best answer so far provided was not entirely satisfactory.
I have examined much of the literature referenced in the SEP article on Many-...
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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 ...
user3164
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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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Appropriate formulation of the necessitation rule from modal logic
The SEP article on modal logic states the necessitation rule for system K (after Saul Kripke):
Necessitation Rule: If A is a theorem of K, then so is □A.
The wikipedia article on modal logic ...
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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 ...
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Modal logic: Are indicative conditionals formulated using a strict conditional?
Given the fact (f) of the actual world
(f) On November 22, 1963: Somebody shot Kennedy.
one could formulat the indicative conditional (id) as follows:
(id) If Oswald did not shoot Kennedy, then ...
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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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What is Ackermanns 'admissibility of gamma' in relevance logic?
Various surveys I've looked at relevance logic mention Ackermanns admissibility of gamma rule. I've not come across the term in logic before, what is it, how is it used and is it also important ...
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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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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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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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Is this a reasonable weak classical Deontic Logic?
I am writing a paper at the moment and an area of Deontic Logic has cropped up in it. I know very little about the area and I was wondering if people could give me opinions on the axiomatic system ...
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I don't understand why Kant's definition of an analytic concept can't be expressed in terms of intensional logic
I've been studying the SEP article about intensional logic, and I think I have a good grasp of what "intension" means. The intension of a term like "bachelor" would be a function that designates a ...
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What is the connection between provability logic & Gödel's first incompleteness theorem?
Provability logic is a modal logic that interprets the modal operator of K as provability and an additional axiom derived from Löb's theorem.
Now the SEP shows that it's possible to derive Gödel's ...
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Understanding "Information States" in Epistemic Modal Logics
I'm having trouble understanding how to interpret the formal apparatus of what appears to be a customary setup for many modal epistemic logics. The setup, found for example in Ifs and Oughts, is as ...
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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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"It is epistemically necessary that P" versus "It is known that P"
Loosely, are the following two statements equivalent?
(1) It is epistemically necessary that P.
(2) It is known that P.
If they are not, in what ways could they be different? I'm thinking in terms ...
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What paradoxes are there for deontic detachment?
Most people agree that if you're going kill someone, then you should kill them gently. Now suppose that you are in fact going to kill them. Then by the statement above, then on a naive application ...
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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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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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Possibly, 7 isn't prime [closed]
I'm curious if in the philosophy of mathematics (or perhaps the philosophy of modality), the following has been proposed:
There exists something like an imaginary (but not complex) number i such ...
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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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Reasoning in S5
I'm currently working on implementing reasoning involving time.
Since S5 (every world accessible from any other) is sufficient for what I'm trying to represent, I wanted to know what are the ...
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One-placed intersection operator
What is the meaning of a formulation like: "A iff ∩A ⊆p"
A is a set of propositions, p is a specific proposition, and the whole formulation is explicated as "There is no possible world where all ...
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For the modal realist, do possible individuals (and worlds) exist necessarily?
For David Lewis's Modal Realism, do the worlds and individuals that inhabit them exist necessarily? In a sense, the answer is "no". For an individual to exist necessarily would be for it to have a ...
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