0
$\begingroup$

I'm trying to write the statement below into first order logic:

My dog Jude is drinking something from the bowl, and everything from the bowl contains germs except for potable water.

I'm using the following predicates Drinks(x,y), From(x,y), Bowl(x), ContainsGerm(x), PotableWater(x).

Not 100% sure about the correctness of the logic and quantifiers that I'm using here, so any advice or suggestion of alternative solution to be discussed is welcome:

$\small\exists x \exists y (({\operatorname{Drinks}(\operatorname{Jude},x)} ~\&~ {\operatorname{Bowl}(y)} ~\&~ {\operatorname{From}(x,y)} ~\&~ (\forall z ({\operatorname{From}(z, y)} ~\&~ {\lnot\operatorname{PotableWater}(z)}) \to \operatorname{ContainsGerm}(z)))$

$\endgroup$
10
  • 1
    $\begingroup$ "the bowl" sounds like an atom. exists y Bowl(y) would more likely be "a bowl" at its first appearance. $\endgroup$ Commented Jun 2, 2022 at 17:32
  • 1
    $\begingroup$ But "Jude" isn't? $\endgroup$ Commented Jun 2, 2022 at 17:59
  • 1
    $\begingroup$ That's fair if those are given requirements, but there's no obvious reason for the difference just from the English, in which both "My dog Jude" and "the bowl" are definite noun phrases. $\endgroup$ Commented Jun 2, 2022 at 18:05
  • 1
    $\begingroup$ Notice the all z part doesn't involve x, so you could rearrange the statement as exists y (exists x (...) & exists z (...)). This rewrite makes sense because once we've identified the bowl in question, the sentence is really the AND of two statements: one about Jude drinking and one about the contents of the bowl. $\endgroup$ Commented Jun 2, 2022 at 18:10
  • 1
    $\begingroup$ 2. Please start using mathjax, as edited (e.g., here) on your behalf in your previous questions. Your latest suggestion, when typed as $$\exists y (\exists x (\text{Drinks}(\text{Jude},x) \land \text{Bowl}(y) \land \text{From}(x,y)) \\\land \forall z (\text{From}(z, y) (\land \lnot\text{PotableWater}(z)) →\text{ContainsGerm}(z))).$$, will display as $$∃y (∃x (\text{Drinks}(\text{Jude},x) \land \text{Bowl}(y) \land \text{From}(x,y)) \\\land (∀z (\text{From}(z, y) \land \lnot\text{PotableWater}(z)) →\text{ContainsGerm}(z))).$$ $\endgroup$ Commented Jun 3, 2022 at 1:19

1 Answer 1

Reset to default
0
$\begingroup$

Given the statement:

My dog Jude is drinking something from the bowl, and everything from the bowl contains germs except for potable water.

The logic representation of it is:

$$\exists y (\exists x (\text{Drinks}(\text{Jude},x) \land \text{Bowl}(y) \land \text{From}(x,y)) \\\land \forall z (\text{From}(z, y) (\land \lnot\text{PotableWater}(z)) →\text{ContainsGerm}(z))).$$

$\endgroup$
1
  • 1
    $\begingroup$ Hope you don't mind my edit (to illustrate what I meant above regarding > versus ` when quoting text). And, more elaborate: $( \big( \Big( \bigg($ gives $( \big( \Big( \bigg(,$ and $∃y() \quad ∃y\,()$ gives $∃y() \quad ∃y\,().$ $\endgroup$ Commented Jun 3, 2022 at 2:06

You must log in to answer this question.

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.