Logic in AI

Logic provides a formal language for representing knowledge and a set of rules for reasoning with that knowledge. It's a cornerstone of symbolic AI, offering a way to make unambiguous statements about the world. Propositional Logic is the simplest form, dealing with propositions—statements that can be either true or false. We can combine these propositions using logical connectives like AND (∧), OR (∨), NOT (¬), and IMPLIES (→). For example, we could state 'p = It is raining' and 'q = I will take an umbrella.' We can then form a rule: 'p → q' (If it is raining, then I will take an umbrella). Using rules of inference, like Modus Ponens, if we know 'p' is true, we can conclude that 'q' is also true. While powerful, propositional logic is limited because it treats propositions as atomic units; it cannot reason about objects, their properties, or relations between them. To address this, First-Order Logic (FOL) extends propositional logic with more expressive concepts. FOL introduces variables (x, y), quantifiers (∀ for 'for all', ∃ for 'there exists'), predicates (properties of objects, e.g., Man(x)), and functions. This allows for much richer statements. For instance, we can say '∀x (Man(x) → Mortal(x))', meaning 'For all x, if x is a man, then x is mortal.' If we then add the fact 'Man(Socrates)', we can logically infer 'Mortal(Socrates)'. FOL provides a powerful framework for building knowledge-based systems that can perform complex reasoning, though the computational cost of inference can be high.