Introduction to Rule-Based Reasoning

1
Introduction to Rule-Based Reasoning

• Jacques Robin

2
Outline

• Rules as a knowledge representation formalism
• Common characteristics of rule-based systems
• Roadmap of rule-based languages
• Common advantages and limitations
• Example practical application of rules
  declarative business rules
• History of rule-based systems
• Production Systems
• Term Rewriting Systems
• Logic Programming and Prolog

3
Rules as a Knowledge Representation Formalism

• What is a rule?
• A statement that specifies that
• If a determined logical combination of
  conditions is satisfied,
• over the set of an agents percepts
• and/or facts in its Knowledge Base (KB)
• that represent the current, past and/or
  hypothetical future of its environment model, its
  goals and/or its preferences,
• then a logico-temporal combination of actions
  can or must be executed by the agent,
• directly on its environment (through actuators)
  or on the facts in its KB.
• A KB agent such that the persistent part of its
  KB consists entirely of such rules is called a
  rule-base agent
• In such case, the inference engine used by the KB
  agent is an interpreter or a compiler for a
  specific rule language.

4
Rule-Based Agent
Environment
Sensors
Ask
Tell
Retract

• Rule Engine
• Problem class independent
• Only dependent on rule language
• Declarative code interpreter or compiler

Ask

• Rule Base
• Persistant intentional knowledge
• Dependent on problem class, not instance
• Declarative code

Effectors
5
Rule Languages Common Characteristics

• Syntax generally
• Extends a host programming language and/or
• Restricts a formal logic and/or
• Uses a semi-natural language with
• closed keyword set expressing logical
  connectives and actions classes,
• and an open keyword set to refer to the entities
  and relations appearing in the agents fact base
• Some systems provide 3 distinct syntax layers
  for different users with automated tools to
  translate a rule across the various layers
• Declarative semantics generally based on some
  formal logic
• Operational semantics
• Generally based on transition systems, automata
  or similar procedural formalisms
• Formalizes the essence of the rule interpreter
  algorithm.

6
Rule Languages General Advantages

• Human experts in many domains (medicine, law,
  finance, marketing, administration, design,
  engineering, equipment maintenance, games,
  sports, etc.) find it intuitive and easy to
  formalize their knowledge as a rule base
• Facilitates knowledge acquisition
• Rules can be easily paraphrased in semi-natural
  language syntax, friendlier to experts averse to
  computational languages
• Facilitates knowledge acquisition
• Rule bases easy to formalize as logical formulas
  (conjunctions of equivalences and/or
  implications)
• Facilitates building rule engine that perform
  sound, logic-based inference
• Each rule largely independent of others in the
  base (but to precisely what degree depends highly
  of the rule engine algorithm)
• Can thus be viewed as an encapsulated,
  declarative piece of knowledge
• Facilitates life cycle evolution and composition
  of knowledge bases
• Very sophisticated, mature rule base compilation
  techniques available
• Allows scalable inference in practice
• Some engines for simple rule languages can
  efficiently handle millions of rules

7
Rule Languages General Limitations

• Subtle interactions between rules hard to debug
  without
• sophisticated rule explanation GUI
• detailed knowledge of the rule engines
  algorithm
• Especially serious with
• Object-oriented rule languages for combining
  rule-based deduction or abduction with
  class-based inheritance
• Probabilistic rule languages for combining
  logical and Bayesian inference
• But purely logical relational rule language do
  not naturally
• Embed within mainstream object-oriented modeling
  and programming languages
• Represent inherently procedural, taxonomic and
  uncertain knowledge
• Current research challenge
• User-friendly reasoning engine for probabilistic
  object-oriented rules

8
Business Rules

• Example of modern commercial application of
  rule-based knowledge representation

9
Semi-Natural Language Syntaxfor Business Rules

• Associate key word or key phrase to
• Each domain model entity or relation name
• Each rule language syntactic construct
• Each host programming language construct used in
  rules
• Substitute in place of these constructs and
  symbols the associated words or phrase
• Example Is West Criminal? in semi-natural
  language syntax
• IF P is American AND P sells a W to N AND
  W is a weapon
• AND N is a nation AND N is hostile
• THEN P is a criminal
• IF nono owns a W AND W is a missile THEN west
  sells W to nono
• IF W is a missile THEN W is a weapon
• IF N is an enemy of America THEN N is hostile

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Roadmap of Rule-Based Languages
11
Rewrite Rules Abstract Syntax
Rewrite Rule Base

• plus(X,0) ? X
• fib(suc(suc(N)))
• ? plus(fib(suc(N)),fib(N))

12
Rewrite Rules Operational Semantics
13
Rewrite Rule Base Computation Example

• plus(X,0) ? X
• plus(X,suc(Y)) ? suc(plus(X,Y))
• fib(0) ? suc(0)
• fib(suc(0)) ? suc(0)
• fib(suc(suc(N)) ? plus(fib(suc(N)),fib(N))

1. fib(suc(suc(suc(0)))) w/ rule
   e?
2. plus(fib(suc(suc(0))),fib(suc(0))) w/ rule d?
3. plus(fib(suc(suc(0))),suc(0)) w/ rule b?
4. suc(plus(fib(suc(suc(0))),0)) w/ rule a?
5. suc(fib(suc(suc(0)))) w/ rule
   e?
6. suc(plus(fib(suc(0)),fib(0))) w/ rule c?
7. suc(plus(fib(suc(0)),suc(0))) w/ rule b?
8. suc(suc(plus(fib(suc(0)),0))) w/ rule a?
9. suc(suc(fib(suc(0)))) w/ rule
   d?
10. suc(suc(suc(0)))

14
Conditional Rewrite RulesAbstract Syntax
Rewrite Rule Base
Rewrite Rule

• X 0 ? Y 0 X Y ? 0

RHS

LHS
Condition

2
Term
Equation

• Rule with matching LHS can only be fired if
  condition is also verified
• Proving condition can be recursively done by
  rewriting it to true

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Rewrite Rule Base Deduction ExampleIs West
Criminal?

• Rewrite Rule Base
• criminal(P) ? american(P) ? weapon(W) ? nation(N)
  ? hostile(N) ? sells(P,N,W)
• sells(west,nono,W) ? owns(nono,W) ? missile(W)
• hostile(N) ? enemy(N,america)
• weapon(W) ? missile(W)
• owns(nono,m1) ? missile(m1) ? american(west) ?
  nation(nono) ? enemy(nono,america) ? true
• A ? B ? B ? A
• A ? A ? A
• Term
• criminal(P)
  
  
• american(P) ? weapon(W) ? nation(N) ? hostile(N)
  ? sells(P,N,W)
  w/ rule a
• american(P) ? weapon(W) ? nation(N) ? hostile(N)
  ? owns(nono,W) ? missile(W) w/
  rule b
• american(P) ? weapon(W) ? nation(N) ?
  enemy(N,america) ? owns(nono,W) ? missile(W) w/
  rule c
• american(P) ? missile(W) ? nation(N) ?
  enemy(N,america) ? owns(nono,W) ? missile(W)
  w/ rule d
• american(P) ? missile(W) ? nation(N) ?
  enemy(N,america) ? owns(nono,W)
  w/ rule g
• 
  ...
  
  w/ rule f
• owns(nono,W) ? missile(W) ? american(P) ?
  nation(N) ? enemy(N,america)
  w/ rule f
• true
  
  
  
  
  w/ rule e
  

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Rewriting Systems Practical Application

• Theorem proving
• CASE
• Programming language formal semantics
• Program verification
• Compiler design and implementation
• Model transformation and automatic programming
• Data integration
• Using XSLT an XML-based language to rewrite
  XML-based data and documents
• Web server pages and web services (also using
  XSLT)

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Production Rules Abstract Syntax
IF (p(X,a) OR p(X,b)) AND
p(Y,Z) AND q(c) AND X ltgt Y AND X gt 3.5 THEN
Z X 12 AND addr(a,c,Z
AND deletep(Y,Z)
Arithmetic Predicate Symbol
Arithmetic Constant Symbol
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Production System Architecture
Fact Base Management Component
Fact Base
Rule Firing Policy Component
Action Execution Component
Pattern Matching Component
Rule Base
Host Language API
Candidate Rules
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Production Rules Operational Semantics
20
Conflict Resolution Strategies

• Conflict resolution strategy
• Heuristic to choose at each cycle which of the
  matching rule set to fire
• Common strategies
• Follow writing order of rules in rule base
• Follow absolute priority level annotations
  associated with each rule or rule class
• Follow relative priority level annotations
  associated with pairs of rules or rule classes
• Prefer rules whose LHS match the most recently
  derived facts in the fact base
• Prefer rules that have remained for the longest
  time unfired while matching a fact
• Apply control meta-rules that declaratively
  specify arbitrarily sophisticated strategies

21
Production Rule Base ExampleIs West Criminal?

• Production Rule Base
• IF american(P) AND weapon(W) AND nation(N) AND
  hostile(N) AND sell(P,N,W)
• THEN addcriminal(P)
• IF owns(nono,W) AND missile(W) THEN
  addsells(west,nono,W)
• IF missile(W) THEN addweapon(W)
• IF enemy(N,america) THEN addhostile(N)
• Initial Fact Base
• owns(nono,m1)
• missile(m1)
• american(west)
• nation(nono)
• enemy(nono,america)
• nation(america)

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Production Rule Inference ExampleIs West
Criminal?
criminal(west)?
criminal(P)
american(P)
weapon(W)
nation(N)
hostile(N)
sells(P,N,W)
sells(west,nono,W)
missile(W)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
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Production Rule Inference ExampleIs West
Criminal?
criminal(west)?
criminal(P)
american(P)
weapon(W)
nation(N)
hostile(N)
sells(P,N,W)
sells(west,nono,W)
missile(m1)
enemy(nono,america)
owns(nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
24
Production Rule Inference ExampleIs West
Criminal?
criminal(west)?
criminal(P)
american(P)
weapon(m1)
nation(N)
hostile(N)
sells(P,N,W)
sells(west,nono,W)
missile(W)
enemy(nono,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
25
Production Rule Inference ExampleIs West
Criminal?
criminal(west)?
criminal(P)
american(P)
weapon(m1)
nation(N)
hostile(N)
sells(P,N,W)
sells(west,nono,W)
missile(m1)
enemy(nono,america)
owns(nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
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Production Rule Inference ExampleIs West
Criminal?
criminal(west)?
criminal(P)
american(P)
weapon(m1)
nation(N)
hostile(nono)
sells(P,N,W)
sells(west,nono,W)
missile(W)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enemy(nono,america)
owns(nono,m1)
nation(america)
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Production Rule Inference ExampleIs West
Criminal?
criminal(west)?
criminal(P)
american(P)
weapon(m1)
nation(N)
hostile(nono)
sells(P,N,W)
sells(west,nono,W)
missile(m1)
owns(nono,m1)
missile(m1)
american(west)
nation(nono)
enemy(nono,america)
owns(nono,m1)
nation(america)
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Production Rule Inference ExampleIs West
Criminal?
criminal(west)?
criminal(P)
american(P)
weapon(m1)
nation(N)
hostile(nono)
sells(P,N,W)
sells(west,nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
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Production Rule Inference ExampleIs West
Criminal?
criminal(west)?
criminal(P)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
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Production Rule Inference ExampleIs West
Criminal?
criminal(west)?
criminal(west)
weapon(m1)
hostile(nono)
sells(west,nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
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Production Rule Inference ExampleIs West
Criminal?
criminal(west)? yes
criminal(west)
weapon(m1)
hostile(nono)
sells(west,nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
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Properties of Production Systems

• Confluence
• From confluent rule base, same final fact base
  is derived independently of rule firing order
• Makes values of queries made to the system
  independent of the conflict resolution strategy
• Termination
• Terminating system does not enter in an infinite
  loop
• Example of non-termination production rule base
• Initial fact base p(0)
• Production rule base IF p(X) THEN Y X 1 AND
  addp(Y)
• Any production system which conflict resolution
  strategy does not prevent the same rule instance
  to be fired in two consecutive cycles is
  trivially non-terminating.

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Production System Inference vs.Lifted Forward
Chaining

• Common characteristics
• Data driven reasoning
• Requires conflict resolution strategy to choose
• Which of several matching rules to fire
• Which of several unifying clauses for next Modus
  Ponens inference step

• Production System Inference
• Sequential conjunction of actions in rule RHS
• Non-monotonic reasoning due to delete actions
• Matching only Datalog atoms (i.e., atoms which
  arguments are all non-functional terms)
• Matching ground fact atoms against non-ground
  atoms in rule LHS And-Or atom
• Neither sound nor complete inference engine

• Lifted Forward Chaining
• Unique conclusion in Horn Clause
• Monotonic reasoning
• Unifying arbitrary first-order atoms, possibly
  functional
• Unifying two arbitrary atoms, possibly both
  non-grounds
• Sound and refutation-complete

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Embedded Production System Abstract Syntax
35
Generalized Production Rules ECA Rules

• Event-Condition-Action rule extension of
  production rule with triggering event external to
  addition of facts in fact base
• Only the rule subset which event just occurred is
  matched against the fact base
• Events thus partition the rule base into subsets,
  each one specifying a behavior in response to a
  given events

Event Condtion Action Rule
LHS
RHS
Event
Agents Percept
HPL Boolean Operation
36
Production Rules vs. Rewriting Rules

• Common characteristics
• Data driven reasoning
• Requires conflict resolution strategy to choose
• Which of several matching rules to fire
• Which of several rules with an LHS unifying with
  a sub-term
• Non-monotonic reasoning due to
• Fact deletion actions in RHS
• Retraction of substituted sub-term
• Tricky confluence and termination issues

• Production System Inference
• Fact base implicitly conjunctive
• Matching only Datalog atoms (i.e., atoms which
  arguments are all non-functional terms)
• Matching ground fact atoms against non-ground
  atoms in rule LHS And-Or atom

• Term Rewriting
• Reified logical connectives in term provide full
  first-order expressivity
• Unifying arbitrary first-order atoms, possibly
  functional
• Unifying two arbitrary atoms, possibly both
  non-grounds

37
Logic Programming a Versatile Metaphor
38
Logic Programming Key Ideas
Logical Theory Software Specification Declarative Programming Automated Reasoning Intelligent Databases
Logical Formula Abstract Specification Declarative Program / Data Structure Knowledge Base Database
Theorem Prover Specification Verifier Interpreter / Compiler Inference Engine Query Processor
Theorem Proof Specification Verification Program Execution Inference Query Execution
Theorem Proving Strategy Verification Algorithm Single, Fixed, Problem-Independent Control Structure Inference Search Algorithm Query Processing Algorithm
39
Logic programming vision

• Single language with logic-based declarative
  semantics that is
• A Turing-complete, general purpose programming
  language
• A versatile, expressive knowledge representation
  language to support deduction and other reasoning
  services useful for intelligent agents
  (abduction, induction, constraint solving, belief
  revision, belief update, inheritance, planning)
• Data definition, query and update language for
  databases with built-in inference capabilities
• "One tool solves all" philosophy
• Any computation resolution unification
  search
• Programming declaring logical axioms (Horn
  clauses)
• Running the program query about theorems
  provable from declared axioms
• Algorithmic design entirely avoided (single,
  built-in control structure)
• Same language for formal specification
  (modeling) and implementation
• Same language for model checking and code testing

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Prolog

• First and still most widely used logic
  programming language
• Falls short to fulfill the vision in many
  respect
• Many imperative constructs with no logical
  declarative semantics
• No commercial deductive database available
• Most other logic programming languages both
• Extend Prolog
• Fulfill better one aspect of the logic
  programming vision
• In the 80s, huge Japanese project tried to
  entirely rebuild all of computing from ground up
  using logic programming as hardware basis

41
Pure Prolog abstract syntax
arg

0..1

Pure Prolog Atom

head
body
Function-Free Term
Functional Term
functor
Variable

• parent(al,jim)
• ? parent(jim,joe)
• ? anc(A,D) ? parent(A,D)
• ? anc(A,D) ? parent(A,P) ? anc(P,D)

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Full Prolog
arg

arg
Prolog Literal
Full Prolog Term

Functional Term
predicate
Function-Free Term
functor
Symbol
User-Defined Symbol
Built-in Symbol
Variable
Built-in Logical Symbol
Built-in Imperative Symbol

• Semantics of full Prolog
• Cannot be purely logic-based
• Must integrate algorithmic ones

Meta-Programming Predicate Symbol
Numerical Symbol
I/O Predicate Symbol
Search Customization Predicate Symbol
Program Update Predicate Symbol
43
Pure Prolog program declarative formal semantics

• Declarative, denotational, intentional
• Clarks transformation to CFOL formula
• First-order formula semantically equivalent to
  program
• Declarative, denotational, extentional,
  model-theoretic
• Least Herbrand Model
• Intersection of all Herbrand Models
• Conjunction of all ground formulas that are
  deductive consequences of program

44
CFOL x Prolog Semantic Assumptions

• Classical First-Order Predicate Logic
• No Unique Name Assumption (UNA) two distinct
  symbols can potentially be paraphrases to denote
  the same domain entity
• Open-World Assumption (OWA) If KB ? Q but KB
  ? ?Q , the truth value of Q is considered
  unknown
• Ex KB true ? core(ai) ? true ? core(se)
  ? core(C) ? offered(C,T) ?
  true ? offered(mda,fall)
• Q true ? offered(mda,spring)
• OWA necessary for monotonic, deductively sound
  reasoning If KB T then ?A, KB ? A T

• Logic Programming
• UNA two distinct symbols necessarily denote two
  distinct domain entities
• Closed-World Assumption (CWA) If KB ? Q but KB
  ? ?Q , the truth value of Q is considered false
• Ex ?- offered(mda,spring) fail
• CWA is a logically unsound form of negatively
  abductive reasoning
• CWA makes reasoning inherently non-monotonic as
  one can haveKB T but KB ? A ? Tif the
  proof KB T included steps assuming A false by
  CWA
• Motivation intuitive, representational economy,
  consistent w/ databases

45
Clarks completion semantics

• Transform Pure Prolog Program P into semantically
  equivalent CFOL formula comp(P)
• Same answer query set derived from P
  (abductively) than from FP (deductively)
• Example Pcore(se). core(ai).
  offered(mda,fall). offered(C,T) - core(C).
• ?- offered(mda,spring)
• no
• ?-

• Naive semantics naive(P)?C,T true ? core(ai)
  ? true ? core(se) ? true ?
  offered(mda,fall) ? core(C) ?
  offered(C,T) naive(P) ? ?offered(mda,spring)
• Clarks completion semantics comp(P)
• ?C,T,C1,T1
• (core(C1) ? (C1ai ? C1se)) ?(offered(C1,T1) ?
  (C1mda ? T1fall) ? (?C,T (C1C
  ? T1T ? core(C)))) ??(aise) ? ?(aimda) ?
  ?(aifall) ? ?(sefall) ? ?(semda) ?
  ?(mdafall)Fp ?offered(mda,spring)

46
Clarks transformation

• Axiomatizes closed-world and unique name
  assumptions in CFOL
• Starts from naive Horn formula semantics of pure
  Prolog program
• Partitions program in clause sets, each one
  defining one predicate (i.e., group together
  clauses with same predicate c(t1, ..., tn) as
  conclusion)
• Replaces each such set by a logical equivalence
• One side of this equivalence contains c(X1, ...,
  Xn) where X1, ..., Xn are fresh universally
  quantified variables
• The other side contains a disjunction of
  conjunctions, one for each original clause
• Each conjunction is either of the form
• Xi ci ? ... ? Xj ci, if the original clause
  is a ground fact
• ?Yi ... Yj Xi Yi ? ... ? Xj Yj ? p1( ...) ?
  ... ? pn( ... ) if the original clause is a rule
  with body p1( ...) ? ... ? pn( ... ) containing
  variables Yi ... Yj
• Joins all resulting equivalences in a conjunction
• Adds conjunction of the form ?(ci cj) for all
  possible pairs (ci,cj) of constant symbols in
  pure Prolog program

47
SLD Resolution

• SLD resolution (Linear resolution with Selection
  function for Definite logic programs)
• Joint use of goal-driven set of support and input
  resolution heuristics
• Always pick last proven theorem clause with next
  untried axiom clause
• Always questions last pick even if unrelated to
  failure that triggered backtracking
• A form of goal-driven backward chaining of Horn
  clauses seen as deductive rules
• Prolog uses special case of SLD resolution where
• Axiom clauses tried in top to bottom program
  writing order
• Atoms to unify in the two picked clauses
• Conclusion of selected axiom clause
• Next untried premise of last proven theorem
  clause in left to right program writing order
  (goal)
• Unification without occur-check
• Generates proof tree in top-down, depth-first
  manner
• Failure triggers systematic, chronological
  backtracking
• Try next alternative for last selection even if
  clearly unrelated to failure
• Reprocess from scratch new occurrences of
  sub-goals previously proven true or false
• Simple, intuitive, space-efficient,
  time-inefficient, potentially non-terminating
  (incomplete)

48
Refutation Resolution Proof Example

• Refutation proof principle
• To prove KB F
• Prove logically equivalent (KB ? F) True
• In turn logically equivalent to (KB ? ? F)
  False
• (american(P) ? weapon(W) ?
• nation(N) ? hostile(N) ?
• sells(P,N,W) ? criminal(P)) //1
• ? (T ? owns(nono,m1)) //2a
• ? (T ? missile(m1)) //2b
• ? (owns(nono,W) ? missile(W) ?
  sells(west,nono,W)) //3
• ? (T ? american(west)) //4
• ? (T ? nation(nono)) //5
• ? (T ? enemy(nono,america)) //6
• ? (missile(W) ? weapon(W)) //7
• ? (enemy(N,america) ? hostile(N))
  //8
• ? (T ? nation(america)) //9
• ? (criminal(west) ? F) //0

1. Solve 0 w/ 1 unifying P/westamerican(west) ?
weapon(W) ? nation(N) ?hostile(N) ?
sells(west,N,W) ? F //10 2. Solve
10 w/ 4weapon(W) ? nation(N) ? hostile(N)
?sells(west,N,W) ? F
//11 3. Solve 11 w/ 7 missile(W) ? nation(N)
? hostile(N) ?sells(west,N,W) ? F
//12 4. Solve 12 w/ 2b unifying
W/m1nation(N) ? hostile(N) ? sells(west,N,m1) ?
F //13 5. Solve 13 w/ 5 unifying
N/nonohostile(nono) ? sells(west,nono,m1) ? F
//14 6. Solve 14 w/ 8 unifying
N/nonoenemy(nono,america) ? sells(west,nono,m1)
? F //15 7. Solve 15 w/ 6 sells(west,nono,m1) ?
F //16 8. Solve 16 w/ 3 unifying W/m1
owns(nono,m1) ? missile(m1) ? F
//17 9. Solve 17 with 2a missile(m1) ? F
//18 10. Solve 18 with 2b F
49
SLD resolution example
criminal(west)?
criminal(P)
american(P)
weapon(W)
nation(N)
hostile(N)
sells(P,N,W)
sells(west,nono,W)
missile(W)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
50
SLD resolution example
criminal(west)?
criminal(west)
american(P)
weapon(W)
nation(N)
hostile(N)
sells(P,N,W)
sells(west,nono,W)
missile(W)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
51
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(W)
nation(N)
hostile(N)
sells(west,N,W)
sells(west,nono,W)
missile(W)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
52
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(W)
nation(N)
hostile(N)
sells(west,N,W)
sells(west,nono,W)
missile(W)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
53
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(W)
nation(N)
hostile(N)
sells(west,N,W)
sells(west,nono,W)
missile(W)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
54
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(W)
nation(N)
hostile(N)
sells(west,N,W)
sells(west,nono,W)
missile(W)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
55
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(W)
nation(N)
hostile(N)
sells(west,N,W)
sells(west,nono,W)
missile(W)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
56
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(W)
nation(N)
hostile(N)
sells(west,N,W)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
57
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(N)
hostile(N)
sells(west,N,W)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
58
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(N)
hostile(N)
sells(west,N,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
59
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(N)
hostile(N)
sells(west,N,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
60
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(N)
hostile(N)
sells(west,N,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
61
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(N)
sells(west,N,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
62
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
63
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
64
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,W)
missile(m1)
enemy(nono,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
65
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,W)
missile(m1)
enemy(nono,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
66
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,W)
missile(m1)
enemy(nono,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
67
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,W)
missile(m1)
enemy(nono,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
68
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,m1)
missile(m1)
enemy(nono,america)
owns(nono,W)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
69
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,m1)
missile(m1)
enemy(nono,america)
owns(nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
70
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,m1)
missile(m1)
enemy(nono,america)
owns(nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
71
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,m1)
missile(m1)
enemy(nono,america)
owns(nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
72
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,m1)
missile(m1)
enemy(nono,america)
owns(nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
73
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,m1)
missile(m1)
enemy(nono,america)
owns(nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
74
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,m1)
missile(m1)
enemy(nono,america)
owns(nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
75
SLD resolution example
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,m1)
missile(m1)
enemy(nono,america)
owns(nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
76
SLD resolution example
criminal(west)? yes
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,m1)
missile(m1)
enemy(nono,america)
owns(nono,m1)
missile(m1)
american(west)
nation(nono)
enermy(nono,america)
owns(nono,m1)
nation(america)
77
SLD resolution example with backtracking
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(N)
hostile(N)
sells(west,N,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(america)
enermy(nono,america)
owns(nono,m1)
nation(nono)
78
SLD resolution example with backtracking
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(N)
hostile(N)
sells(west,N,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(america)
enermy(nono,america)
owns(nono,m1)
nation(nono)
79
SLD resolution example with backtracking
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(america)
hostile(N)
sells(west,N,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(america)
enermy(nono,america)
owns(nono,m1)
nation(nono)
80
SLD resolution example with backtracking
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(america)
hostile(america)
sells(west,america,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(america)
enermy(nono,america)
owns(nono,m1)
nation(nono)
81
SLD resolution example with backtracking
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(america)
hostile(america)
sells(west,america,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(america)
enermy(nono,america)
owns(nono,m1)
nation(nono)
82
SLD resolution example with backtracking
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(america)
hostile(america)
sells(west,america,m1)
sells(west,nono,W)
missile(m1)
owns(nono,W)
enemy(america,america)
missile(m1)
american(west)
nation(america)
enermy(nono,america)
owns(nono,m1)
nation(nono)
83
SLD resolution example with backtracking
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(america)
hostile(america)
sells(west,america,m1)
sells(west,nono,W)
enemy(america,america)
missile(m1)
owns(nono,W)
fail
missile(m1)
american(west)
nation(america)
enermy(nono,america)
owns(nono,m1)
nation(nono)
84
SLD resolution example with backtracking
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(america)
hostile(america)
sells(west,america,m1)
sells(west,nono,W)
backtrack
missile(m1)
enemy(N,america)
owns(nono,W)
fail
missile(m1)
american(west)
nation(america)
enermy(nono,america)
owns(nono,m1)
nation(nono)
85
SLD resolution example with backtracking
criminal(west)?
criminal(west)
backtrack
american(west)
weapon(m1)
nation(N)
hostile(N)
sells(west,N,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(america)
enermy(nono,america)
owns(nono,m1)
nation(nono)
86
SLD resolution example with backtracking
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(N)
hostile(N)
sells(west,N,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(america)
enermy(nono,america)
owns(nono,m1)
nation(nono)
87
SLD resolution example with backtracking
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(N)
sells(west,N,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(america)
enermy(nono,america)
owns(nono,m1)
nation(nono)
88
SLD resolution example with bactracking
criminal(west)?
criminal(west)
american(west)
weapon(m1)
nation(nono)
hostile(nono)
sells(west,nono,m1)
sells(west,nono,W)
missile(m1)
enemy(N,america)
owns(nono,W)
missile(m1)
american(west)
nation(america)
enermy(nono,america)
owns(nono,m1)
nation(nono)
89
Limitations of Pure Prolog and ISO Prolog

• For programming
• no fine-grained encapsulation
• no code factoring (inheritance)
• poor data structures (function symbols as only
  construct)
• mismatch with dominant object-oriented paradigm
• not integrated to comprehensive software
  engineering methodology
• IDE not friendly enough
• scarce middleware
• very scarce reusable libraries or components (ex,
  web, graphics)
• mono-thread
• For declarative logic programming
• imperative numerical computation, I/O and
  meta-programming without logical semantics

• For knowledge representation
• search customization
• No declarative constructs
• Limited support procedimental constructs (cuts)
• no support for uncertain reasoning
• forces unintuitive rule-based encoding of
  inherently taxonomic and procedural knowledge
• knowledge base updates non-backtrackable and
  without logical semantics
• ab - assert(a), b.if b fails, a remains as true

90
Limitation of SLD resolution engines

• Unsound unification without occur-check
• Incomplete left-recursion
• Correct ancestor Prolog program
• anc(A,D) - parent(A,D).
• anc(A,D) - parent(P,D), anc(A,P).
• Logically equivalent program (since conjunction
  is a commutative connective) that infinitely
  loops anc(A,D) - anc(A,P), parent(P,D).
  anc(A,D) - parent(A,D).
• Inefficient
• repeated proofs of same sub-goals
• irrelevant chronological backtracking

91
Prologs imperative arithmetics

• fac(0,1) - !.
• fac(I,O) - I1 is I - 1,
• fac(I1,O1), O is I O1.
• ?- fac(1,X).
• X 1
• ?- fac(3,X).
• X 6
• ?- I1 is I -1
• error
• ?- I1 I -1
• I1 I -1
• ?- I 2, I1 I -1
• I1 2 -1
• ?- I 2, I1 is I -1
• I1 1

• Arithmetic functions and predicates generate
  exception if queried with non-ground terms as
  arguments
• is requires a uninstantiated variable on the
  left and an arithmetic expression on the right
• Relational programming property lost
• Syntax more like assembly than functional !
• is Prologs sole explicit variable assignment
  predicate (only for arithmetics)
• is a bi-directional, general-purpose
  unification query predicate

92
Prologs redundant sub-goal proofs
93
Extensions of pure Prolog
Aleph
Inductive LP
Abductive LP
Preference LP
Functional LP
Pure Prolog
Constraint LP
ISO Prolog
XSB
High-Order LP
Tabled LP
Transaction LP
Flora
Frame (OO) LP
94
Constraint Logic Programming (CLP)

• CSP libraries strengths
• Specification level, declarative programming for
  predefined sets of constraints over given domains
• Efficient
• Extensive libraries cover both finite domain
  combinatorial problems and infinite numerical
  domain optimization problems
• CSP libraries weaknesses
• Constraint set extension can only be done
  externally through API using general-purpose
  programming language
• Same problem for mixed constraint problems (ex,
  mixing symbolic finite domain with real
  variables)

• Prologs strengths
• Allows specification level, declarative
  programming of arbitrary general purpose problems
• A constraint is just a predicate
• New constraints easily declaratively specified
  through user predicate definitions
• Mixed-domain constraints straightforwardly
  defined as predicate with arguments from
  different domains
• Prologs weakness
• Numerical programming is imperative, not
  declarative
• Very inefficient at solving finite domain
  combinatorial problem

95
CLP

• Integrate Prolog with constraint satisfaction and
  solving libraries in a single inference engine
• Get the best of both worlds
• Declarative user definition of arbitrary
  constraints
• Declarative definition of arbitrarily mixed
  constraints
• Declarative numerical and symbolic reasoning,
  seamlessly integrated
• Efficient combinatorial and optimization problem
  solving
• Single language to program constraint
  satisfaction or solving problems and the rest of
  the application

CLP Application Rule Base
CLP Engine
Prolog Engine
...
Procedural Solver for Domain D1
Procedural Solver for Domain Dk
Solver Programming Language L
Prolog/L Bridge