Discrete Math/ Logic
How do we represent the above facts in 1)axiom form and 2)clausal form
1) All babies are innocent 2) Anyone who is innocent and affectionate will be loved by others 3) Anyone who is loved by others, will receive gifts 4) Teena is an affectionate baby
My thoughts on the question : (Let Vx and Ex denote universal and existential quantifiers respectively )
Let B(x) denote x is a baby I(x) denote x is innocent A(x) denote x is affectionate L(x) denote x is loved by others G(x) denote x receives a gift
Axiom Form : 1) Vx[ B(x) --> I(x) ] 2) Vx[ I(x) ^ A(x) ] --> L(x) 3) Vx [ L(x) --> G(x) ] 4) B(Teena) --> A(Teena)
Have I done the first part correctly? And how do we do the second part?
Thanks!
Answers
ch10_logic2a.pdf
22 October 2019
http: Hi ashley760,Regarding axiom form, you're on the right track, but there are some errors. First, your translation of (2) is incorrect, because the third variable should be bound by the quantifier. So, (2) should be replaced with 'Vx [ [ I(x) & A(x) ] > Lx ]'. Second, your translation of (4) is incorrect, because it says 'if Teena is a baby then Teena is affectionate', not 'Teena is an affectionate baby' (note that the truth of the former is compatible with the falsity of the latter because the antecedent could be false). So, (4) should be replaced with 'B(Teena) & A(Teena)'.Third, unless the logic you are working with contains only unary predicates (i.e., does not contain binary predicates), then (2) and (3) are incorrect (even given my above correction), because they are not fine-grained enough. So, you should replace the translation of 'L' with 'L(y,x) = y loves x', (2) should be replaced with 'Vx Vy [ [ I(y,x) & A(x) ] > Lx ]', and (3) should be replaced with 'Vx Vy [ L(y,x) > G(x)]'. If you interpret 'is loved by others' as 'is loved by some others', rather than 'is loved by all others' as I have done, then replace the relevant universal quantifier with an existential quantifier.Regarding the translation from axiom form to clausal form, see the attached document and/or link: https://ocw.mit.edu/courses/health-sciences-and-technology/hst-947-medical-artificial-intelligence-spring-2005/lecture-notes/ch10_logic2a.pdfI hope this helps.Best wishes,Matt.
22 October 2019
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