Questions tagged [modal-logic]
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69
questions
9
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0answers
195 views
Sum and Product game
Two perfect logicians Steve and Pete, who have never met, before are imprisoned by an eccentric villain. "I have two positive integer numbers x and y" he says to them. "I will tell Steve the sum x+y, ...
0
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0answers
79 views
Expressing a model transformation by using monads in the simply-typed lambda calculus
In https://link.springer.com/content/pdf/10.1007/s10670-019-00128-z.pdf , page 16, the following clause is given for a modal operator $\langle R_k \rangle$ (see definition 4.2 for the definition of a ...
0
votes
0answers
11 views
Are all simple models from modal logic ($M_1 p \to M_2 p$) canonical?
I'm reading an interesting on modal logic by Timothy Surendonk [1], where he defines the concept of canonical logic as the following.
A logic $L$ is defined to be canonical if there's a frame $\...
15
votes
1answer
749 views
Are buttons really enough to bound validities by S4.2?
Joel Hamkins recently claimed on twitter that buttons suffice to bound the validities of a potentialist system to the modal logic S4.2 (see here), and that switches are not necessary. We have been ...
4
votes
1answer
104 views
In modal logic, is there a formula that could express the inverse of accessibility relation?
For example, in S4, is there a formula that corresponds to the proposition "p is true in every world from which u is accessible (but is not accessible from u)"?
5
votes
0answers
159 views
Definable modal logics in first-order structures
The old version didn't ask the right question and was also terribly written; see the edit history if interested. Also: throughout, formulas are allowed parameters, and when I say "definable subset of $...
10
votes
0answers
292 views
Connection between Provability Logic (GL) and geometry?
In Provability Logic (aka GL) we have
The Beth definability theorem and
De Jong-Sambin Fixed Point Theorem
The former has a vague similarity to the implicit function theorem in that you can loosely ...
0
votes
1answer
104 views
Superintuitionistic logics which are not hereditary/monotonic: impossible or possible?
An intuitionistic Kripke model is a triple $\langle W,\leq, \Vdash \rangle$, where $\langle W,\leq \rangle$ is a preordered Kripke frame, and
$\Vdash$ satisfies the following condition of ...
2
votes
1answer
163 views
What is the dual of generating Boolean subalgebra by subexpressions of a modal formula?
I am supposed to be answering this question rather than asking it but I really cannot figure out.
There is a variation on Stone duality linking algebraic and (descriptive) Kripke semantics for (...
3
votes
0answers
117 views
Modal Principles of Field Extensions
In 2007 (with more work done later), J. Hamkins and B. Löwe found that the ZFC provably valid principles of forcing are the assertions of S4.2. In the introduction, they mention field extension as a ...
1
vote
0answers
70 views
Looking for help in defining a new epistemic logic
I'm looking for some guidance in defining a new epistemic, temporal logic.
I am looking to extend a logic called Sequential Epistemic Logic (SPAL): https://pdfs.semanticscholar.org/dae6/...
3
votes
3answers
457 views
How can you formalize the metamathematics conventionally used to state Godel’s theorem?
Gödel’s incompleteness theorem states that for any sufficiently strong formal system $T$ there exists a statement $G$ such that if $T$ is consistent, then $G$ is true but not provable in $T$. But I’m ...
16
votes
1answer
1k views
What is the modal logic of outer multiverse?
The mathematical multiverse could be viewed as a gigantic Kripke model with models of $ZFC$ as possible worlds connected to each other via a certain accessibility relation.
The modal logic associated ...
4
votes
1answer
163 views
Axioms for modal logics based upon counterfactuals
Suppose we have a logic for counterfactuals as with David Lewis. I here use $\Rrightarrow$ for the counterfactual conditional. So suppose we have:
Rules:
(1) If $A$ and $A\rightarrow B$ are ...
1
vote
0answers
82 views
Limits in subcategories of Powerset-coalgebras
Let $F:Set\to Set$ be a functor. An $F$-coalgebra is a pair $\mathcal{A}=(A,\alpha)$ where $\alpha:A\to F(A)$ is arbitrary map.
Given $F$-coalgebras $\mathcal{A}=(A,\alpha)$ and $\mathcal{B}=(B,\beta)$...
1
vote
1answer
139 views
Translations between S4 and S5 modal logics
$\textbf{Question}$: Is there a translation from $\textbf{S5}$ modal logic to $\textbf{S4}$ such that
$$\text{If} \hspace{0.3cm} \textbf{S5} \vdash F \hspace{0.3cm} \text{then } \hspace{0.3cm} \...
2
votes
0answers
64 views
Substructural shuffling: can we avoid a modal collapse in a certain Intuitionistic modal logic via making the logic linear?
Consider Propositional Lax Logic ($PLL$)
https://www.uni-bamberg.de/fileadmin/uni/fakultaeten/wiai_professuren/grundlagen_informatik/papersMM/pll.pdf
The Hilbert system of $PLL$ takes as axiom ...
2
votes
1answer
211 views
Can we avoid the modal collapse in a certain Intuitionistic modal logic by abandoning ¬◯⊥ but retaining the law of the excluded middle?
Consider Propositional Lax Logic ($PLL$)
https://www.uni-bamberg.de/fileadmin/uni/fakultaeten/wiai_professuren/grundlagen_informatik/papersMM/pll.pdf
The Hilbert system of $PLL$ takes as axiom ...
2
votes
1answer
152 views
Modal collapse upon addition of the law of the excluded middle to an Intuitionistic modal logic
Consider Propositional Lax Logic ($PLL$)
https://www.uni-bamberg.de/fileadmin/uni/fakultaeten/wiai_professuren/grundlagen_informatik/papersMM/pll.pdf
The Hilbert system of $PLL$ takes as axiom ...
9
votes
0answers
366 views
The Curry Howard Isomorphism and models for an intuitionistic modal logic and its bimodal translation
My question regards the Curry Howard Isomorphism and how it constrains models in the case of a particular logic.
Consider quantified Lax Logic $QLL$.
https://pdfs.semanticscholar.org/468e/...
8
votes
0answers
194 views
A bi-modal logic related to determinacy
The short version of my question is as follows. There is a natural (I hope!) way to associate a bimodal theory to a game (two-player, perfect-information, length-$\omega$, on $\omega$); are there "...
1
vote
0answers
41 views
Is there a restriction of Linear Temporal Logic that has a “Markov” property?
I have a problem, that I can formulate as model-finding in Linear Temporal Logic (via Büchi automata). I also have the additional knowledge, that there is always satisfied a Markov-like property, ...
22
votes
1answer
792 views
Is the axiom $\Diamond\Box\varphi\to\Box\Diamond\varphi$ in c.c.c. forcing potentialism equivalent to the productivity of c.c.c. forcing?
This question arose in connection with a lecture series on
Potentialism
that I have just completed here in Hejnice in the Czech Republic at
the Winter School 2018 (see
Slides). Several of us discussed ...
8
votes
1answer
369 views
Substitutional modality
An informal definition of a logical truth is a sentence that's true in virtue of its form alone: $\phi$ is logically true iff all substitutions of $\phi$ that leave its logical vocabulary alone are ...
1
vote
0answers
88 views
Are all normal modal logics isomorphic to this type of algebras?
Consider a Boolean set algebra on a set $\Omega$. Let $\sigma$ be a set function on $\Omega$ such that for all $m\in \Omega$ $\sigma(m)\subset \Omega$. The operator $\square_\sigma$ is defined by $\...
1
vote
0answers
118 views
How do I express a second order restriction upon a third order comprehension schema?
I want a third order $\Pi^2_1$-comprehension schema so that $\alpha$ in
$$\forall x_1,\ldots,x_k, X_1,\ldots,X_l,\Psi_1,\ldots,\Psi_m\exists \Upsilon\forall Y(\Upsilon Y\Leftrightarrow\forall \Phi\...
6
votes
1answer
587 views
Modal vs First-Order Logic on finite models
It is known that Modal Logic can be interpreted in First-Order logic via Standard translation. However, this translation needs a unary predicate for every propositional variable. It is also known that ...
1
vote
0answers
79 views
Question on deriving $\diamond \alpha \rightarrow \diamond \diamond\alpha$ in modal logic S4-system [closed]
I can't seem to achieve this derivation.
The other way around, so $\diamond \diamond \alpha \rightarrow \diamond\alpha$, I did. But could someone helpt me with this part?
1
vote
1answer
193 views
Modal logic in combination with automata theory
I'm planning to write a paper about the possibility of describing modal logic and the multiple world aspect of it with techniques of automata theory. To not duplicate my work does anyone have more ...
5
votes
2answers
269 views
Literature on Kripke models
Which is the best introduction to Kripke-models for modal logics?
I am a M.Sc in mathematics and know predicatlogic.
3
votes
1answer
194 views
What kind of set theory is obtained from the canonical models of K?
Consider the minimal normal modal logic $K$ (axioms = classical propositional logic + $(\Box(p\land q)\leftrightarrow\Box p\land\Box q)$ + $(\Box\top)$, nothing else).
Its canonical model with no ...
1
vote
1answer
310 views
Does being an Euclidean relation imply being a Shift-Reflexive relation? [closed]
Let me start with a few basic definitions.
Let $X$ be any set. A relation $R\subseteq X\times X$ is:
Euclidean when $$\forall x,y,z\in X: (x,y)\in R\,\wedge\,(x,z)\in R\, \rightarrow\,(y,z)\in R$$
...
0
votes
1answer
151 views
Proving satisfiability in modal logic [closed]
So I've been doing some self study on Modal logic and I would like some external input on how to present my proofs for some of the axioms
1) say for example I am told to prove that □phi implies ♢psi ...
3
votes
1answer
480 views
How to get $\omega$-regular expression from buchi automaton
Is there an algorithm or a trick on how to get $\omega$-regular expressions from Buchi automatons? If yes, is there also some way to do create minimal such regular expressions?
It is extremely ...
0
votes
0answers
169 views
Minimum regular open set containing a given set in a T0 Alexandrov topological space
What is known about the minimum regular open set containing a given set in a T$_0$ Alexandrov topological space? I'm particularly interested in the condition for the minimum set happening to be first-...
0
votes
1answer
244 views
A question on two modal formulas
I want to find out the correspondences for the following two formulas or whether they are already derivable in the modal logic $KD4.2$, i.e. whether the formulas are valid in serial, transitive and ...
3
votes
2answers
491 views
Is there a good list of nomenclature for modal axioms?
I would like to see what names that has been suggested for useful modal axioms. By name here I mean some abbreviation such as $T$, $K$, $4$, $.2$, $E$ and so on. In particular I am interested in ...
1
vote
0answers
208 views
This modal logic semantics is not S5, but is it something else well-known?
The short form of the question is this:
Is there a model of modal propositional calculus that gives the modal operators the meanings
...
1
vote
0answers
189 views
Kripke frames as classes of partitions
Here's something I've been playing with off and on for a bit; I'm curious if anyone has seen it before.
For this question, a Kripke frame $K$ is a finite reflexive directed graph. (Reflexivity isn't ...
6
votes
2answers
796 views
A specific Model of ZFC
In his paper "Some Second Order Set Theory", Joel Hamkins asked whether there is a model of set theory $V$ that is elementary equivalent to $V[G]$, Whenever $G$ is $V$-generic for the collapse of a ...
2
votes
1answer
119 views
A question on Carnap's modal semantics on the basis of Cochiarelli's primary semantics
I believe I learned that Carnap's state description semantics for propositional modal logic suffered from validating $\lozenge p$ for all atomic variables p. Re-reading Nino Cochiarelli's primary ...
1
vote
0answers
149 views
Interesting fragments of first-order logic induced by sorting?
In first approximation, modal logic (I'm using the term loosely)
can be understood as an interesting fragment of first-order logic
(for simplicity I ignore e.g. how modal logic relates to
...
2
votes
1answer
547 views
Is this system incomplete?
Let $\mathbf{SBM}$ be the normal modal logic system defined as $\mathbf{T}$ plus the following two axioms:
$$\mathrm{SB}: \Box(\Diamond p \rightarrow p)\rightarrow (p \rightarrow \Box p)$$
$$\mathrm{...
2
votes
1answer
170 views
Question on deriving $\alpha \rightarrow \Box \alpha$ in modal logic KTU
Let K and T be the usual modal logical principles $\Box (\alpha \rightarrow \beta) \rightarrow (\Box \alpha \rightarrow \Box \beta)$ and $\Box \alpha \rightarrow \alpha$. Let U be the modal logical ...
4
votes
2answers
338 views
On a modal correspondence
Is there an intuitive characterization of the correspondence for the modal logical formula $\square (\alpha \rightarrow \square \alpha) \rightarrow (\square \alpha \vee \square \lnot \alpha)$?
In ...
4
votes
1answer
352 views
On directedness, transitivity and ancestral directedness
Let $\textit{C}$ be the modal logical schema $(\square (\square \alpha \rightarrow \alpha) \wedge \square (\square \lnot\alpha \rightarrow \lnot \alpha))\rightarrow (\square \alpha \vee \square \lnot \...
2
votes
0answers
78 views
A question on completeness for quantified temporal logics
Quantified temporal logics have the Barcan formulas and its converses for both G (it will always be the case that) and H (it has always been the case that), so that both $\forall x G \alpha \...
7
votes
1answer
282 views
Is a computer program for correspondence theory available?
In the 1990s I some times used a computer program with the Max Planck Institute which helped with calculating complicated correspondences for modal logical formulas. Is some program like that ...
2
votes
0answers
46 views
Completeness results for quantified tense logics with BF?
Modal tense logics or temporal logics are important in that they correspond with partial orders and their extensions.
Are there completeness results for quantified temporal logics with the Barcan ...
3
votes
0answers
76 views
A question on the incompleteness of quantified K.2 and S4.2 with the Barcan formula
I have been attempting to come to grips with Max Cresswell's account of this in Journal of Philosophical Logic 24 (4):379 - 403 (1995) where he presents proofs of the incompleteness of QK.2BF as well ...
