first-order-logic

来源： https://stackoverflow.com/questions/64325939/first-order-logic-creating-terms-for-arithmetic-expressions-using-prolog

问题 My intuition says that it is not possible to translate the sentence all red cars are better than all blue cars into description logics (in FOL this would be ∀x∀y (red(x) ∧ blue(y) → better(x,y)) interpreted in the domain of cars). Indeed, the only construction that is a complete binary relation containing all pairs of elements of the domain is the universal role U . I don't see how to ask for all pairs of elements of the set red on the left and elements of the set blue on the right, i.e., how

问题 I've encountered a question asking whether the flowing sentence is valid/contingent/unsatisfiable: p(x)⇒∀x.p(x) I think the answer is the sentence is valid. under section 6.10 of the textbook here http://logic.stanford.edu/intrologic/secondary/notes/chapter_06.htmlsays a sentence with free variables is equivalent to the sentence in which all of the free variables are universally quantified. Therefore I think the first relational sentence p(x) is equal to ∀x.p(x) and therefore the sentence is

问题 I am studying binary trees in Prolog. I know the structure but I don't understand this code in my slides: binary_tree(void). binary_tree(tree(_Element,Left,Right)) :- binary_tree(Left), binary_tree(Right). This would need for recognize the tree structure. But does "void" represent? I tried this query ?- binary_tree(a). false. and assume that a is one node of a tree. I'm following this resource for understanding: https://sites.google.com/site/prologsite/prolog-problems/4 but is different to my

问题 I've been looking at various SMT solvers, mainly Z3, CVC4, and VeriT. They all have vague descriptions of their ability to solve SMT problems with quantifiers. Their documentation is primarily example based (Z3), or consists of academic papers, describing possible changes that may or may not actually be implemented. I know that there are decidable fragments of First-order logic, such as: Finitely-bounded quantifiers Monadic first-order logic What I'd like to know is, which (if any) classes of