Introduction
In Artificial Intelligence (AI), the ability of machines to reason, interpret, and derive knowledge relies heavily on the principles of Knowledge Representation and Reasoning (KR&R). KR&R provides a framework through which facts about the world are captured and used to make logical decisions. At the heart of this framework lie three essential pillars: syntax, semantics, and inference.
Syntax ensures that statements are well-formed according to logical rules.
Semantics provides meaning by connecting statements to truth values in the real world.
Inference allows machines to deduce new knowledge from existing information.
These three components are deeply interconnected and collectively make logical reasoning possible.
Syntax: The Rules of Formation
Syntax refers to the formal structure or grammar of the logical language used in knowledge representation. It defines the rules for forming well-formed formulas (WFFs) using symbols, variables, connectives, and quantifiers. It determines whether a sequence of symbols is a valid sentence in the logical system.
Role of Syntax
Ensures precision by restricting arbitrary combinations of symbols.
Helps in distinguishing valid logical formulas from meaningless symbol strings.
Provides the foundation upon which semantics and inference can operate.
Example in Propositional Logic
Well-formed: (P∨Q)∧R
Not well-formed: (∨PRQ)
Example in First-Order Logic (FOL)
Well-formed: ∀x(Human(x)→Mortal(x))
Not well-formed: ∀(x Human)⇒Mortal
Semantics: Meaning and Truth
Semantics assigns meaning to syntactically correct statements by interpreting them in a model.
A model consists of a domain of objects and an interpretation function that assigns values to symbols.
Truth values (True/False) are then computed based on these interpretations.
Role of Semantics
Provides a bridge between symbols and the real-world situations they describe.
Allows AI systems to check whether a statement correctly represents reality.
Ensures logical statements are not just grammatically valid but also meaningful.
Example in Propositional Logic
Let:
P: "It is raining"
Q: "The ground is wet"
Sentence: (P→Q)
• True if whenever P is true, Q is also true.
• False if P is true but Q is false.
Truth Table for Implication
| P |
Q |
P → Q |
| T |
T |
T |
| T |
F |
F |
| F |
T |
T |
| F |
F |
T |
Example in First-Order Logic
Sentence: ∀x(Human(x)→Mortal(x))
Model: Domain = {Socrates, Plato}, Human = {Socrates, Plato}, Mortal = {Socrates, Plato}
True in this model because all humans are mortals.
Inference: Deriving New Facts
Inference is the process of generating new logical conclusions from existing statements using rules of reasoning.
Role of Inference
Enables knowledge bases to be expanded dynamically.
Helps AI systems draw conclusions that were not explicitly stated.
Soundness and Completeness
Soundness: Only derives conclusions that are true in all models.
Completeness: If a conclusion is true in all models, inference can derive it.
Example: Modus Ponens
Premise 1: P→Q
Premise 2: P ("It is raining").
Conclusion: Q ("The ground is wet").
This rule ensures valid conclusions can be drawn systematically.
Interconnection of Syntax, Semantics, and Inference
These three components function together as a pipeline:
Syntax checks whether a sentence is well-formed.
Semantics determines its truth in a model.
Inference derives new facts from a combination of true sentences.
For example:
Syntax validates that (P∧Q) →R is a well-formed statement.
Semantics confirms whether it holds true in a given world (e.g., if both P and Q are true, then R must be true).
Inference uses this to derive R from P∧Q.
Applications in AI
Expert Systems: Syntax ensures consistent knowledge bases; semantics links rules to real-world facts; inference derives diagnoses or recommendations.
Natural Language Processing (NLP): Syntax governs grammatical structure; semantics captures meaning; inference aids in question answering.
Robotics: Robots use syntax to encode sensor rules, semantics to interpret them, and inference to make decisions.
Case Study: Medical Expert System
Semantics: Interpretations based on patient symptoms.
Inference: If a patient has fever and cough, infer flu.