Question

Logic problem：

Symbolize in the language of First-Order Logic, using the dictionary provided below.

Symbolize in the language of First-Order Logic, using the dictionary provided below. DICTIONARY · m = MITS (The Man In The Street) . w= wITS (The Woman in the Street) · 1=Logic · Lx = x is a logician . PX-x is a pacifist Mx-x is a man . .Wx-x is a woman Rxy-x respects y Lxy = x loves y Sxy x is smarter than y 1. Some pacifists do not respect logicians who are smarter than they are. 2. Some women respect logicians but not pacifists. 3. Some pacifists are smarter than all logicians. 4. There is a logican whom both MITS and WITS respect 5. Any logician that respects women also respects men 6. Not all women who love logicians respect pacifists who are smarter than they are 7. Some pacifists only love logicians who respect all women. Using the dictionary provided above, express the following in plain, idiomatic English

Answer 1

Solution:

1. $\exists x: Px \land (\forall y: Ly \land Syx \rightarrow \neg Rxy )$

2. $\exists x: Wx \land (\forall y: Ly \land \neg Py \rightarrow Rxy )$

3. $\exists x: Px \land (\forall y: Ly \rightarrow Sxy)$

4. $\exists x: Lx \land (\forall m \forall w: Rmx \land Rwx)$

5.

6. $\exists w: Ww \land (\forall l: Ll \rightarrow Lwl) \land (\forall p: Pp \land Spw \land \neg Rwp)$

7. $\exits p: Pp \land \forall l: Ll \land (Lpl \rightarrow \forall w: Ww \land Rlw)$