introduction to artificial intelligence massimo poesio lecture 4: semantic networks and description...
TRANSCRIPT
INTRODUCTION TO ARTIFICIAL INTELLIGENCE
Massimo Poesio
LECTURE 4: Semantic Networks and Description Logics
SEMANTIC NETWORKS• Around end of the ’70s researchers in Psychology thought
they had found evidence that knowledge was organized more or less as expected on the basis of ideas about taxonomies
• This led to the development of formalisms for knowledge representation in AI called SEMANTIC NETWORKS
• Soon researchers like Schubert (1975) and Hayes (1979) demonstrated that these formalisms were just notational variants of logic
• The ‘logical’ approach to semantic networks has however led to the development of so-called DESCRIPTION LOGICS, a family of logics which also includes logics with better computational properties than first order logic
SOME RESULTS FROM COGNITIVE PSYCHOLOGY: SEMANTIC NETWORKS
• Collins & Quillian, 1969: knowledge appears to be organized around objects and in a taxonomic way– A canary is yellow– A canary has feathers– A canary eats food
• Haviland & Clark 1974, Sanford & Garrod 1979: ‘associated’ knowledge available when concepts are mentioned– I looked around the house.– The lounge was very spacious.
SEMANTIC NETWORKS
• Hypothesis: commonsense knowledge is organized in networks whose nodes are types and instances of types, and whose relations encode– Taxonomic relations (as in Aristotle)– Attributes
• The key inference that such theories want to model: INHERITANCE– Semantic networks also called INHERITANCE
NETWORKS
AN EXAMPLE OF SEMANTIC NETWORK
ANIMALeats food
can move
BIRD FISH
CANARY
can fly
has feathers
yellow
sings
swims
scales
DESCRIPTION LOGICS
• Brachman & Levesque (1985) proposed a formal approach to knowledge bases organized as semantic networks, encoding inheritance reasoning
SPECIFYING A KNOWLEDGE BASE: TBOX AND ABOX
• According to Description Logics, a knowledge base contains two types of knowledge:– Generic knowledge about concepts, contained in
the TBOX (ie: SEMANTIC MEMORY)• Bicycles have two wheels• Parents have children
– Knowledge about the instances of these concepts, contained in the ABOX (ie: EPISODIC MEMORY)
• Massimo’s bicycle is grey
• Distinct logical languages for each of them
CONCEPT DEFINITION SYNTAX• Intersection of concepts: C ∩ D
– E.g., ANIMAL ∩ FLY– Interpretation: ANIMAL(x) ∩ CANFLY(x)
• Attributes: R.C∃– E.g., hasFeather.FEATHER∃
• Value restriction: R.C∀– E.g., hasWheel.WHEEL∀
• Number restriction: (≤ n R), (≥ n R)– E.g., (≤ 2 hasWheel)
• Negation: ¬ C– E.g., ¬ FEMALE
EXAMPLES OF COMPLEX CONCEPTS
• BIRD ∩ YELLOW ∩ SINGS• ANIMAL ∩ RATIONAL• PERSON ∩ ¬ FEMALE• VEHICLE ∩(≤ 2 hasWheel)• VEHICLE ∩ hasEngine.ENGINE∃•
TBOX DEFINITIONS
• NECESSARY AND SUFFICIENT– CANARY ≡ BIRD ∩ YELLOW ∩ SINGS– HUMAN ≡ ANIMAL ∩ RATIONAL– WOMAN ≡ PERSON ∩ FEMALE– MALE ≡ PERSON ∩ ¬ FEMALE– BICYCLE ≡ VEHICLE ∩(≤ 2 hasWheel) ∩
¬ hasEngine.ENGINE∃
• PRIMITIVE– BEAR ANIMAL⊂
SEMANTICS
• TBOX concepts denote SETS– ∩ denotes INTERSECTION– ¬ denotes COMPLEMENTATION– Etc
• The resulting language is a subset of FOL
INFERENCE IN DL
• Description Logics were developed to model inheritance reasoning
• In fact, they model a more complex form of reasoning: SUBSUMPTION
• They are intended to be the COMPUTATIONALLY LEAST EXPENSIVE logics in which such reasoning is possible
SUBSUMPTION
• Concept D subsumes concept C, written
C D⊆• If D is MORE GENERAL than C, i.e., if the set
denoted by C is a subset of the set denoted by D
EXAMPLE OF (TBOX) SUBSUMPTION: INHERITANCE
CANARY ≡ BIRD ∩ YELLOW ∩ CANSING
∴ CANARY CANFLY⊆
BIRD≡ ANIMAL ∩ CANFLY∩ hasFeather.FEATHER∃
EXAMPLE OF (TBOX) SUBSUMPTION
CAR≡ VEHICLE ∩(= 4 hasWheel) ∩ hasEngine.ENGINE∃
∴ CAR ENGINED_OBJECT ⊆
ENGINED_OBJECT ≡ hasEngine.ENGINE∃
SUBSUMPTION AND MODERN PSYCHOLOGICAL THEORIES OF CONCEPTUAL KNOWLEDGE
• As we will see in the next lectures, modern theories of concepts in cognitive science (since Rosch) have abandoned the position that conceptual knowledge is organized taxonomically in favour of the `clustering’ views from PROTOTYPE THEORY
• Subsumption is a modern approach to inheritance that does NOT depend on the existence of special ISA links
UNDECIDABILITY, COMPLEXITY, and LOGIC
• One would want to have a logic as expressive as possible – ideally, as expressive as natural language
• But there is a tight connection between the expressive power of a logic and the cost of reasoning with that logic
• It is known from Goedel and Turing that FOL is undecidable
• Even the propositional calculus is NP-complete
THE COMPLEXITY OF DESCRIPTION LOGICS
• The simplest form of DL is DECIDABLE and POLYNOMIAL (i.e., relatively efficient)
• But even minor additions result in exponential complexity
• DL-FOL is undecidable