Bài giảng Hệ chuyên gia (Expert System): Chương 2.2 - PGS.TS. Phan Huy Khánh

Bài giảng Hệ chuyên gia (Expert System) - Chương 2.2 đề cập đến lôgic mệnh đề. Trong chương này sẽ trình bày 2 nội dung chính, đó là các khái niệm lôgic và lôgic mệnh đề. Mời các bạn cùng tham khảo để nắm bắt các nội dung chi tiết.
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Bài giảng Hệ chuyên gia (Expert System): Chương 2.2 - PGS.TS. Phan Huy KhánhHệ chuyên gia (Expert System) PGS.TS. Phan Huy Khánh khanhph@vnn.vn Chương 2 Biểu diễn tri thức nhờ logic vị từ bậc một 2.2 Chương 2 Biểu diễn tri thức nhờ logic vị từ bậc mộta Phần 2.2 : V Khái niệm lôgic V Lôgic mệnh đề 2/68 The 4 Color Theorema In 1879, Kempe produced a famous proof of the 4 color theorem: V Using only 4 colors V Any map of countries can be colored in such a way that no 2 bordering countries have the same colora In 1890, Heawood showed: V The proof not to be a proof at all!a When is a proof a proof, and when is it not a proof?a Logic to the rescue! 3/68 What is the logic?a Logic is the science of reasoning, proof, thinking, or inferencea Logic allows us to analyze a piece of reasoning and determine whether it is correct or nota To use the technical terms, we determine whether the reasoning is valid or invalida When people talk of logical arguments, though, they generally mean the type being described here 4/68 Logica Logic is the study of reasoninga In particular: V Logic studies the conditions under which we can say that a piece of reasoning is valid V I.e. that something (the conclusion) can be said to follow from something else (the premises, givens, assumptions)a Ontology (ont = ‘to be’; logica = ‘word’): kinds of things one can talk about in the language 5/68 Arguments in Logica What is an Argument? V An argument is a connected series of statements intended to establish a proposition“a An argument refers to the formal way facts and rules of inferences are used to reach valid conclusionsa The process of reaching valid conclusions is referred to as logical reasoning 6/68 Logic in generala A logic is a formal system of representing knowledgea Logics are formal languages for representing information such that conclusions can be drawna Syntax defines the sentences (statements) in the languagea Semantics define the meaning of sentences V i.e., define truth of a sentence in a worlda Proof theory V How conclusions are drawn from a set of statements 7/68 Deduction and Inductiona If the conclusion has to be true assuming the truth of the premises, we call the reasoning deductivea If the conclusion is merely more likely to be true than false given the truth of the premises, we call the reasoning inductivea Logic studies both deduction and induction, but does tend to focus on deduction, especially formal logic 8/68 Normative and Descriptive Theories of Reasoninga Psychology of reasoning is a scientific study of how humans reason: V What do humans infer from what? V What is the mechanism behind human reasoning?a As such, psychologists come up with descriptive theories of reasoning: hypotheses as to how humans reason based on empirical studies.a Logicians, however, try to come up with normative theories of reasoning: V What actually follows from what?a Question: But if not empirical, what is the basis for such theories? (Human!) reason alone? 9/68 Implication and Trutha Logic tells us about implication, not trutha Example: V “All flurps are toogle, but not all flems are toogle, so not all flems are flurps” is perfectly logical, but tells us nothing about what-is- the-case.a One exception: V Implication itself can be seen as a kind of (necessary) truth V So, logic can tells us that certain statements of the form “If then ” are necessarily true (i.e. true in all possible worlds), and hence true in our world as well 10/68 Logic and Sciencea Of course, if I do know that my premises are true, then if the reasoning is (deductively) valid I know the conclusion to be true as wella But that’s just science: science combines observation (facts) with logic (reasoning), to get to truth (laws of physics, chemistry, etc)a Of course, scientific reasoning is inherently inductive: a finite set of data is always compatible with multiple the ...