I have the following predicates:
- Doctor(D)
- Hospital(H)
- WorksIn(D, H)
- HasShift(D, IdS, H)
Is this FOL formula transformation correct? I'm a little unsure.
Every doctor that works in hospitals has at least two different shifts
2026-04-04 01:59:02.1775267942
First Order Logic formula transformation
55 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in LOGIC
- Theorems in MK would imply theorems in ZFC
- What is (mathematically) minimal computer architecture to run any software
- What formula proved in MK or Godel Incompleteness theorem
- Determine the truth value and validity of the propositions given
- Is this a commonly known paradox?
- Help with Propositional Logic Proof
- Symbol for assignment of a truth-value?
- Find the truth value of... empty set?
- Do I need the axiom of choice to prove this statement?
- Prove that any truth function $f$ can be represented by a formula $φ$ in cnf by negating a formula in dnf
Related Questions in FIRST-ORDER-LOGIC
- Proving the schema of separation from replacement
- Find the truth value of... empty set?
- Exchanging RAA with double negation: is this valid?
- Translate into first order logic: "$a, b, c$ are the lengths of the sides of a triangle"
- Primitive recursive functions of bounded sum
- Show formula which does not have quantifier elimination in theory of infinite equivalence relations.
- Logical Connectives and Quantifiers
- Is this proof correct? (Proof Theory)
- Is there only a finite number of non-equivalent formulas in the predicate logic?
- How to build a list of all the wfs (well-formed sentences)?
Related Questions in PREDICATE-LOGIC
- Find the truth value of... empty set?
- What does Kx mean in this equation? [in Carnap or Russell and Whitehead's logical notation]
- Exchanging RAA with double negation: is this valid?
- Logical Connectives and Quantifiers
- Is this proof correct? (Proof Theory)
- Is there only a finite number of non-equivalent formulas in the predicate logic?
- Are Proofs of Dependent Pair Types Equivalent to Finding an Inverse Function?
- How to build a list of all the wfs (well-formed sentences)?
- Translations into logical notation
- What would be the function to make a formula false?
Related Questions in QUANTIFIERS
- Show formula which does not have quantifier elimination in theory of infinite equivalence relations.
- Prove or disprove: $\exists x \forall y \,\,\varphi \models \forall y \exists x \,\ \varphi$
- Variables, Quantifiers, and Logic
- Express least and greatest fixed point using predicate and quantifiers
- Nested Quantifiers - Excluding Self
- Logical Equivalences Involving Quantifiers
- Translating Propositional Functions
- Valid Set builder notations for simple set.
- Explanation about quantifier sequence ∀x∃y and ∃y∀x
- Contrapositive of a quantified statement
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- 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?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- 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
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Your translation is probably what they were looking for, but the English sentence is actually somewhat ambiguous.
Note that in your translation, any doctor ends up working two shifts for every hospital they work at. So, for example, if a doctor works at 3 different hospitals, then that doctor will end up having a total of 6 shifts or more.
Now, this interpretation is probably the one that they meant, but it is also possible to read the sentence as: any doctor who works at any hospitals at all (so they work at at least one hospital), will have a total of at least two shifts. So with that interpretation, a doctor working at 3 different hospitals could end up working still only 2 shifts total (somehow distributed among those hospitals).
Now, I would say that given the use of language, together with common sense and knowledge regarding doctors, hospitals, and shifts, the former interpretation is more likely the one that was meant, in which case your translation is correct. But, it would be an interesting exercise for yourself to try and logically translate the second interpretation: the first-order logic sentence for that ends up being a little more complicated.