First-order logic —also called predicate logic, predicate calculus, quantificational logic —is a collection of formal systems used in mathematics, philosophy, linguistics, and computer …

对两个公式 p 和 q, θ 是一个代换, 若有 SUBST(θ, p) = SUBST(θ, q), 则代换 θ 被称为 p 和 q 的合一(Unifier), 寻找合一的算法称作合一算法 UNIFY. 例如： UNIFY(Knows(John,x), …

一阶逻辑（First-Order Logic, FOL）是数学和计算机科学中广泛使用的逻辑系统，它允许我们描述和推理关于个体、集合及其关系的复杂结构。在并发系统中，这种逻辑可以用来定义进程的行 …

1998年10月14日 · Horn clauses represent a subset of the set of sentences representable in FOL. For example, P(a) v Q(a) is a sentence in FOL but is not a Horn clause. Natural deduction …

There exist complete and sound proof procedures for propositional and FOL. Use the definition of entailment directly. Proof procedure is exponential in n, the number of symbols. In practice, …

2016年5月30日 · 实际上，一阶逻辑是一种形式系统（Formal System)，即形式符号推理系统，也叫一阶谓词演算、低阶谓词演算(Predicate Calculus）、限量词（Quantifier）理论，也有人称 …

Example: FOL formula ∀x. p(f(x),x) → (∃y. p(f(g(x,y)),g(x,y)) | {z } G) ∧ q(x,f(x)) | {z } F The scope of ∀x is F. The scope of ∃y is G. The formula reads: “for all x, if p(f(x),x) then there exists a y …

2024年10月9日 · In this chapter, you’ll learn about first order logic (FOL), which is the benchmark for logical systems. FOL is one of the most expressive logic systems in widespread use, and it …

inference procedure for unrestricted FOL • Reminder: Resolution rule for propositional logic: – P 1 ∨ P 2 ∨ ... ∨ P n – ¬P 1 ∨ Q 2 ∨ ... ∨ Q m – Resolvent: P 2 ∨ ... ∨ P n ∨ Q 2 ∨ ... ∨ Q m • We’ll …

First-Order Logic (FOL) • Over the same language <a,b,p>, FOL possible worlds include: • Objects: A p true for A • Objects: the real numbers b — 3.14159. p true for all rational numbers …