Knowledge Representation and Logical Reasoning
Symbolic AI
Why logic matters
Symbolic representation enables explicit structure, compositionality, and interpretable inference. In AI, logic is useful when correctness, explanation, and constraint satisfaction are central.
Key logic concepts
Reasoning tasks and complexity
| Task | Typical formalism | Computational challenge |
|---|---|---|
| SAT | Propositional logic | NP-complete |
| SMT | SAT plus theories | Often harder in practice |
| First-order theorem proving | FOL | Semi-decidable |
| Model checking | Temporal logic | State explosion |
Expressiveness trade-off
Increasing expressiveness often increases inferential complexity; a central research theme is finding fragments that balance tractability and modeling power.
Which statement best describes completeness in deductive reasoning?
Completeness means all semantically entailed conclusions are derivable in the proof system.
Correct answer: Every true sentence can be proved by the system.
Why is first-order logic more expressive than propositional logic?
Quantifiers and predicates let FOL represent structure that propositional logic cannot compactly encode.
Correct answer: It quantifies over objects and relations, allowing general statements about domains of arbitrary size.
Symbolic reasoning paradigms
Forward chaining
- Data-driven
- Useful for rule systems
- Can generate many intermediate facts
Backward chaining
- Goal-driven
- Efficient when the query is specific
- Common in logic programming
Building a knowledge-based AI system
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Step 1: Choose the representational language.
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Step 2: Encode domain facts and inference rules.
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Step 3: Define queries and consistency constraints.
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Step 4: Select a solver or theorem prover.
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Step 5: Validate outputs against ground truth and counterexamples.