Representation of syntax, semantics and Predicate logics
- 1. Representation of Syntax, Semantics and Predicate logics Prof. Neeraj Bhargava Kapil Chauhan Department of Computer Science School of Engineering & Systems Sciences MDS University, Ajmer
- 2. Text Semantics • In Natural Language Processing (NLP), semantics is concerned with the meanings of texts. • There are two main approaches: • Propositional or formal semantics: A block of text is to converted into a formula in a logical language, e.g. predicate calculus. • Vector representation. Texts are embedded into a high- dimensional space.
- 3. Representation AI agents deal with knowledge (data) Facts (believe & observe knowledge) Procedures (how to knowledge) Meaning (relate & define knowledge) Right representation is crucial Early realisation in AI Wrong choice can lead to project failure Active research area
- 4. Some General Representations Logical Representations Production Rules Semantic Networks • Conceptual graphs, frames Description Logics
- 5. What is a Logic? A language with concrete rules No ambiguity in representation (may be other errors!) Allows unambiguous communication and processing 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)
- 6. 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 five foot tall” A valid sentence (syntax) And we can understand the meaning (semantics) This sentence happens to be false (there is a counterexample)
- 7. Propositional Logic Syntax Propositions, e.g. “it is wet” Connectives: and, or, not, implies, iff (equivalent) Brackets, T (true) and F (false) Semantics 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
- 8. 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) In predicate logic each atom is a predicate e.g. first order logic, higher-order logic
- 9. Representation & Logic AI wanted “non-logical representations” Production rules Semantic networks Conceptual graphs, frames But all can be expressed in first order logic! Best of both worlds Logical reading ensures representation well-defined Representations specialised for applications Can make reasoning easier, more intuitive
- 10. Assignment Explain predicate logic with example.