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Questions tagged [modal-logic]

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2
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1answer
74 views

Validity of a modal argument about “vagueness”

(2nd version to make explicit my implicit assumptions about A, B and C, and the definitions of the non-logical constants "⊂" and "≡".) Intuitively, the following modal argument seems valid to me and ...
4
votes
2answers
152 views

What does the category of RDF models look like in Institution Theory?

The Question in short Here is the question in its pure form. Details of my reasoning can be found below. The RDF1.1 spec semantics defines a model to consist of a set IR of objects and IP of ...
3
votes
1answer
67 views

Multimodal logic with quantification over modal operators

I take a multimodal logic to be a logic with multiple (potentially infinitely many) primitive modal operators. I am curious if anyone has studied a logic that allows one to quantify over the modal ...
8
votes
1answer
371 views

Complexity of modal logic IK5

What is the complexity of local satisfiability problem for modal logic $\mathit{IK5}$? Herein we denote by $IK5$ the modal logic over euclidean frames extended with inverse modality. Could you provide ...
5
votes
1answer
224 views

Proof that the theory of rationals is convex

In Example 10.12 of the book The calculus of computation by Bradley and Manna, it is said The theory of rationals is convex, as it is convex in a geometric sense. How does the geometric sense of ...
1
vote
1answer
78 views

How to model degree variable in logic (new type of modal logic?)?

I am trying to model domain in logic (first order logic or some of modal logics) and I have variable which is degree and not true-false variable. There can be different conclusions depending on the ...
5
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0answers
186 views

Are there any logics to formalize understanding?

Are there any logics (modal-based or others) to formalize the following statement: "agent A understands p". For example "agent A understands that Titanic sank because it hit an iceberg" Where "...
6
votes
0answers
279 views

Is there a name for this property of a binary relation?

Consider a binary relation $\mathsf{R}$ such that $x\mathsf{R}y$ is the case only if there is some $z$ such that both $x\mathsf{R}z$ and $y\mathsf{R}z$ are the case. (EDIT: note that this may be ...
3
votes
1answer
229 views

What is the descriptive complexity of the basic modal logic?

This is kind of multiple questions in one. Let's consider $\phi$ a formula in the basic modal language (that is, in propositional language based on a set of propositional variables $\Phi$, plus one of ...
2
votes
0answers
74 views

Regaining decidability by adding axioms that model real world situation

It is known that first order logic is too general to be decidable. Adding axioms with special meaning (e.g. expressing notions such as necessity/obligation, provability, etc.) leads us to modal logics ...
1
vote
1answer
110 views

Is there good open source project that apply semantic web, modal logics, and similar technologies

Recently such themes as semantic web, modal logics, business rules have seen increased interest as research topics in computer science (alhough many of then have more than 80 years of history), but ...
2
votes
1answer
179 views

Explanation of states, models and worlds in Kripke semantics?

Can someone explain to me how the concepts of states, models and worlds work together in Kripke semantics? I've been trying to piece together how the parts work are linked together but cannot figure ...
12
votes
2answers
344 views

Modal logics axiomatised with nesting depth one which are unlikely to be in PSPACE?

I am looking for modal logics, which are axiomatised by a finite set of axioms of modal nesting depth one, and whose satisfiability / derivability problem is unlikely to be in PSPACE. Without the ...
15
votes
1answer
342 views

Looking for papers and articles on the Tarskian Möglichkeit

Some background: Łukasiewicz many-valued logics were intended as modal logics, and Łukasiewicz gave an extensional definition of the modal operator: $\Diamond A =_{def} \neg A \to A$ (which he ...