Notes From CS Undergrad Courses FSU
This project is maintained by awa03
The theory of size and calculation posits that one method of solving problems is to try all possible answers, however this is inefficient. This gave birth to heuristics. Conceptual abstraction is a difficult task in a AI development, and we still really dont know how to conceptualize and instruct on how to perform it. Randomness and creativity are another challenge, getting the program to have creativity requires it to think abstractly as well as hypothetically.
Some powerful tools were developed in order to assist with the creation of AI, for example, LISP and PROLOG.
Abstraction is an essential tool for managing complexity as well as an important factor in assuring that the resulting programs are somewhat efficient. Expressiveness may need to be sacrificed in some manner in order to improve efficiency. Take for example floating point numbers. A representational scheme should be able to express all needed information while maintaining efficiency.
Predicate Calculus provides artificial intelligence with a well defined language. In predicate calculus, predicates are used to express properties or relations between objects, and quantifiers (e.g., ∀, ∃) are employed to specify the scope of these predicates.
Semantic networks can be expressed via predicate calculus. They maybe used to show grouping. Semantic networks are a type of knowledge representation scheme used to model relationships between concepts, objects, and ideas. They consist of nodes (vertices) and links (edges) between nodes, where nodes represent entities and links represent relationships between them. We assume an inheritance relationship within these graphs.
A major component of intelligent problem solving is search. State space search is a major area of search, an example of this maybe a chess player. Chess players consider their opponents moves as well as possible short term gain moves. Deciding the best solution requires all of these options to be weighted. State space diverges at every possible move. Consider tick tack toe. A state space of tic tac toe would encompass every possible move, and the search would determine the best move to make. We add heuristics in order to make this process more efficient, as well as remove some nonsensical searches.
What is a formal logic system? It consists of a language for expressions (formulas, expressions, statements), a collection of these are chose to serve as axioms, and inference rules. Once we have defined our formal system next we need to determine semantics. We need to say "What does the statement mean" and then derive whether the system is true or not.
Soundness (Consistency): If an expression is a theorem, then it is true Adequacy (Completeness): If an expression is true, then it is a theorem.
If a formal system is sound and complete with respects to its semantics then the inference rule is valid.