Suppose we are evaluating $\square p$, $\diamondsuit$p, $\square\square$p, $\diamondsuit\diamondsuit$p, $\square$$\diamondsuit$p, $\diamondsuit$$\square$p on a dead end world (the world that can't reach any further worlds). Are all of these trivially true or are some of them false, and if so, why? Thanks in advance.
2025-01-13 07:58:26.1736755106
Necessity and sufficiency on dead end worlds in Kripke's model
151 Views Asked by Glavatar https://math.techqa.club/user/glavatar/detail AtRelated Questions in LOGIC
- how does complicated truth tables work?
- Implication in mathematics - How can A imply B when A is False?
- Different Quantifiers, same variable
- Elimination of quantifiers in the strucure of polynomials and in the structure of exponentials
- What are the prerequisites for "Systems of Logic Based on Ordinals (1938)" by Turing?
- Help with Prover9 for weak propositional systems
- State machine scenario: finding invariant
- “You cannot... unless...” and “You can... only if...”
- Quantifiers and If then statements
- Show that $\forall x\varphi\vDash\varphi[t/x]$ may not hold if $t$ is bound for $x$ in $\varphi$.
Related Questions in MODAL-LOGIC
- Proof set of a sentence (error in textbook?)
- Modal logic of contingency and necessity operators?
- Validity at state w
- Replacing equivalent formulas and Rule N in epistemic logic
- Finding a condition on models that validate theorems
- Nested Sets of Points
- Validity of $ F \supset \Box F$
- Canonical models for systems
- Proving completeness of modal systems
- Show that the canonical modal for the modal logic s4.3 has no branching to the right
Related Questions in KRIPKE-MODELS
- Validity of $ F \supset \Box F$
- Is Kripke/relational/possible world semantics the special case of the the set semantics or first order logic?
- Is the statement $(\exists x\psi(x)\rightarrow\forall x\theta(x))\vdash \forall x(\psi(x)\rightarrow\theta(x))$ true in intuitionistic/minimal logic?
- Why is $\lozenge (p\to p)$ not valid in system $K$ of modal logic?
- Proofing transitivity of simulation relation in Kripke structures
- Accessibility relation in non-classical logics: hereditary or not?
- Semantic explanation for converting intuitionistic logic into classical logic by adding LEM as an axiom
- Necessity and sufficiency on dead end worlds in Kripke's model
- I am looking for a soundness, completeness and consistency proof for this particular $S5$ calculus.
- Are there any invalid $S5$-formulas $\psi$ such that $\diamond\psi$ is valid?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity