Artificial Intelligence Knowledge Representation 2023
Artificial Intelligence Knowledge Representation 2023. What is a Logic? A language with concrete rules – No ambiguity in representation (may be other errors!) – Allows unambiguous communication and processing – Very unlike natural languages e.g. English Many ways to translate between languages – A statement can be represented in different logics – And perhaps differently in same logic Expressiveness of a logic – How much can we say in this language? Not to be confused with logical reasoning – Logics are languages, reasoning is a process (may use logic) Syntax and Semantics Syntax – Rules for constructing legal sentences in the logic – Which symbols we can use (English: letters, punctuation) – How we are allowed to combine symbols Semantics – How we interpret (read) sentences in the logic – Assigns a meaning to each sentence Example: “All lecturers are seven foot tall” – A valid sentence (syntax) – And we can understand the meaning (semantics) – This sentence happens to be false (there is a counterexample) Propositional Logic Syntax – Propositions, e.g. “it is wet” – Connectives: and, or, not, implies, iff (equivalent) – Brackets, T (true) and F (false) Semantics (Classical AKA Boolean) – Define how connectives affect truth “P and Q” is true if and only if P is true and Q is true – Use truth tables to work out the truth of statements Predicate Logic Propositional logic combines atoms – An atom contains no propositional connectives – Have no structure (today_is_wet, john_likes_apples) Predicates allow us to talk about objects – Properties: is_wet(today) – Relations: likes(john, apples) – True or false In predicate logic each atom is a predicate – e.g. first order logic, higher-order logic
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