Logic Programming

1
Logic Programming

• Raul Cruz-Cano

2
Announcements
3
Logic Programming

• the use of mathematical logic for computer
  programming.
• In this view of logic programming, which can be
  traced at least as far back as John McCarthy's
  1958 advice-taker proposal
• It was probably the first proposal to use logic
  to represent information in a computer and the
  first paper to propose common sense reasoning
  ability as the key to artificial intelligence.
• In his paper, McCarthy advocated
• "programs to manipulate in a suitable formal
  language common instrumental statements. The
  basic program will draw immediate conclusions
  from a list of premises. These conclusions will
  be either declarative or imperative sentences.
  When an imperative sentence is deduced the
  program takes a corresponding action."
• Logic is used as a purely declarative
  representation language, and a or
  model-generator is used as the problem-solver.

4
Logic Programming

• The problem-solving task is split between
• the programmer, who is responsible only for
  ensuring the truth of programs expressed in
  logical form, and
• the theorem-prover or model-generator, which is
  responsible for solving problems efficiently.

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Prolog

• The programming language Prolog was developed in
  1972 by Alain Colmerauer (Marseille) and Robert
  Kowalski (Edinburgh)
• Colmerauer was working on natural language
  understanding, using logic to represent semantics
  and using resolution for question-answering.
• During the summer of 1971, they discovered that
  the clausal form of logic could be used to
  represent formal grammars and that resolution
  theorem provers could be used for parsing.
• It was in the following summer of 1972, that
  Kowalski, again working with Colmerauer,
  developed the procedural interpretation of
  implications which later became formalised in the
  Prolog notation

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Learn Prolog Now!
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GNU Prolog

• Freely available Prolog interpreter
• Works with Windows,
• There are many more Prolog interpreters
• Not all are ISO compliant

8
Lecture

• Theory
• Introduction to Prolog
• Facts, Rules and Queries
• Prolog Syntax
• Exercises
• Exercises of LPN chapter 1
• Practical work

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Aim of this lecture

• Give some simple examples of Prolog programs
• Discuss the three basic constructs in Prolog
• Facts
• Rules
• Queries
• Introduce other concepts, such as
• the role of logic
• unification with the help of variables
• Begin the systematic study of Prolog by defining
  terms, atoms, and variables

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Prolog

• "Programming with Logic"
• Declarative
• Very different from other (procedural)
  programming languages
• Good for knowledge-rich tasks

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History of Prolog
first Prolog interpreter by Colmerauer and Roussel
1972
1980s/1990s
1977
1980
2005
12
History of Prolog
implementation of DEC10 compiler by Warren
1972
1980s/1990s
1977
1980
2005
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History of Prolog
Definite Clause Grammars implementation by
Pereira and Warren
1972
1980s/1990s
1977
1980
2005
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History of Prolog
Prolog grows in popularity especially in Europe
and Japan
1972
1980s/1990s
1977
1980
2005
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History of Prolog
Prolog used to program natural language interface
in International Space Station by NASA
1972
1980s/1990s
1977
1980
2005
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Basic idea of Prolog

• Describe the situation of interest
• Ask a question
• Prolog logically deduces new facts about the
  situation we described
• Prolog gives us its deductions back as answers

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Consequences

• Think declaratively, not procedurally
• Challenging
• Requires a different mindset
• High-level language
• Not as efficient as, say, C
• Good for rapid prototyping
• Useful in many AI applications

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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

?-
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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

?- woman(mia).
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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

?- woman(mia). yes ?-
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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

?- woman(mia). yes ?- playsAirGuitar(jody).
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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

?- woman(mia). yes ?- playsAirGuitar(jody). yes ?-
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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

?- woman(mia). yes ?- playsAirGuitar(jody). yes ?-
playsAirGuitar(mia). no
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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

?- tattoed(jody).
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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

?- tattoed(jody). no ?-
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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

?- tattoed(jody). ERROR predicate tattoed/1 not
defined. ?-
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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

?- party.
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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

?- party. yes ?-
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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

?- rockConcert.
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Knowledge Base 1

• woman(mia).
• woman(jody).
• woman(yolanda).
• playsAirGuitar(jody).
• party.

?- rockConcert. no ?-
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Knowledge Base 2

• happy(yolanda).
• listens2music(mia).
• listens2music(yolanda)- happy(yolanda).
• playsAirGuitar(mia)- listens2music(mia).
• playsAirGuitar(yolanda)- listens2music(yolanda).

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Knowledge Base 2
fact

• happy(yolanda).
• listens2music(mia).
• listens2music(yolanda)- happy(yolanda).
• playsAirGuitar(mia)- listens2music(mia).
• playsAirGuitar(yolanda)- listens2music(yolanda).

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Knowledge Base 2
fact

• happy(yolanda).
• listens2music(mia).
• listens2music(yolanda)- happy(yolanda).
• playsAirGuitar(mia)- listens2music(mia).
• playsAirGuitar(yolanda)- listens2music(yolanda).

fact
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Knowledge Base 2
fact

• happy(yolanda).
• listens2music(mia).
• listens2music(yolanda)- happy(yolanda).
• playsAirGuitar(mia)- listens2music(mia).
• playsAirGuitar(yolanda)- listens2music(yolanda).

fact
rule
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Knowledge Base 2
fact

• happy(yolanda).
• listens2music(mia).
• listens2music(yolanda)- happy(yolanda).
• playsAirGuitar(mia)- listens2music(mia).
• playsAirGuitar(yolanda)- listens2music(yolanda).

fact
rule
rule
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Knowledge Base 2
fact

• happy(yolanda).
• listens2music(mia).
• listens2music(yolanda)- happy(yolanda).
• playsAirGuitar(mia)- listens2music(mia).
• playsAirGuitar(yolanda)- listens2music(yolanda).

fact
rule
rule
rule
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Knowledge Base 2

• happy(yolanda).
• listens2music(mia).
• listens2music(yolanda)- happy(yolanda).
• playsAirGuitar(mia)- listens2music(mia).
• playsAirGuitar(yolanda)- listens2music(yolanda).

head
body
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Knowledge Base 2

• happy(yolanda).
• listens2music(mia).
• listens2music(yolanda)- happy(yolanda).
• playsAirGuitar(mia)- listens2music(mia).
• playsAirGuitar(yolanda)- listens2music(yolanda).

?-
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Knowledge Base 2

• happy(yolanda).
• listens2music(mia).
• listens2music(yolanda)- happy(yolanda).
• playsAirGuitar(mia)- listens2music(mia).
• playsAirGuitar(yolanda)- listens2music(yolanda).

?- playsAirGuitar(mia). yes ?-
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Knowledge Base 2

• happy(yolanda).
• listens2music(mia).
• listens2music(yolanda)- happy(yolanda).
• playsAirGuitar(mia)- listens2music(mia).
• playsAirGuitar(yolanda)- listens2music(yolanda).

?- playsAirGuitar(mia). yes ?- playsAirGuitar(yola
nda). yes
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Clauses

• happy(yolanda).
• listens2music(mia).
• listens2music(yolanda)- happy(yolanda).
• playsAirGuitar(mia)- listens2music(mia).
• playsAirGuitar(yolanda)- listens2music(yolanda).

There are five clauses in this knowledge
base two facts, and three rules. The end of a
clause is marked with a full stop.
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Predicates

• happy(yolanda).
• listens2music(mia).
• listens2music(yolanda)- happy(yolanda).
• playsAirGuitar(mia)- listens2music(mia).
• playsAirGuitar(yolanda)- listens2music(yolanda).

There are three predicates in this knowledge
base happy, listens2music, and playsAirGuitar
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Knowledge Base 3

• happy(vincent).
• listens2music(butch).
• playsAirGuitar(vincent)- listens2music(vincent),
  happy(vincent).
• playsAirGuitar(butch)- happy(butch).
• playsAirGuitar(butch)- listens2music(butch).

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Expressing Conjunction

• happy(vincent).
• listens2music(butch).
• playsAirGuitar(vincent)- listens2music(vincent),
  happy(vincent).
• playsAirGuitar(butch)- happy(butch).
• playsAirGuitar(butch)- listens2music(butch).

The comma ," expresses conjunction in Prolog
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Knowledge Base 3

• happy(vincent).
• listens2music(butch).
• playsAirGuitar(vincent)- listens2music(vincent),
  happy(vincent).
• playsAirGuitar(butch)- happy(butch).
• playsAirGuitar(butch)- listens2music(butch).

?- playsAirGuitar(vincent). no ?-
47
Knowledge Base 3

• happy(vincent).
• listens2music(butch).
• playsAirGuitar(vincent)- listens2music(vincent),
  happy(vincent).
• playsAirGuitar(butch)- happy(butch).
• playsAirGuitar(butch)- listens2music(butch).

?- playsAirGuitar(butch). yes ?-
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Expressing Disjunction

• happy(vincent).
• listens2music(butch).
• playsAirGuitar(vincent)- listens2music(vincent),
  happy(vincent).
• playsAirGuitar(butch)- happy(butch).
• playsAirGuitar(butch)- listens2music(butch).

happy(vincent). listens2music(butch). playsAirGuit
ar(vincent)- listens2music(vincent),
happy(vincent). playsAirGuitar(butch)-
happy(butch) listens2music(butch).
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Prolog and Logic

• Clearly Prolog has something to do with logic
• Operators
• Implication -
• Conjunction ,
• Disjunction
• Use of modus ponens
• Negation

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Knowledge Base 4

• woman(mia).
• woman(jody).
• woman(yolanda).
• loves(vincent, mia).
• loves(marsellus, mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).

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Prolog Variables

• woman(mia).
• woman(jody).
• woman(yolanda).
• loves(vincent, mia).
• loves(marsellus, mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).

?- woman(X).
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Variable Instantiation

• woman(mia).
• woman(jody).
• woman(yolanda).
• loves(vincent, mia).
• loves(marsellus, mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).

?- woman(X). Xmia
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Asking Alternatives

• woman(mia).
• woman(jody).
• woman(yolanda).
• loves(vincent, mia).
• loves(marsellus, mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).

?- woman(X). Xmia
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Asking Alternatives

• woman(mia).
• woman(jody).
• woman(yolanda).
• loves(vincent, mia).
• loves(marsellus, mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).

?- woman(X). Xmia Xjody
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Asking Alternatives

• woman(mia).
• woman(jody).
• woman(yolanda).
• loves(vincent, mia).
• loves(marsellus, mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).

?- woman(X). Xmia Xjody Xyolanda
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Asking Alternatives

• woman(mia).
• woman(jody).
• woman(yolanda).
• loves(vincent, mia).
• loves(marsellus, mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).

?- woman(X). Xmia Xjody Xyolanda no
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Knowledge Base 4

• woman(mia).
• woman(jody).
• woman(yolanda).
• loves(vincent, mia).
• loves(marsellus, mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).

?- loves(marsellus,X), woman(X).
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Knowledge Base 4

• woman(mia).
• woman(jody).
• woman(yolanda).
• loves(vincent, mia).
• loves(marsellus, mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).

?- loves(marsellus,X), woman(X). Xmia yes ?-
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Knowledge Base 4

• woman(mia).
• woman(jody).
• woman(yolanda).
• loves(vincent, mia).
• loves(marsellus, mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).

?- loves(pumpkin,X), woman(X).
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Knowledge Base 4

• woman(mia).
• woman(jody).
• woman(yolanda).
• loves(vincent, mia).
• loves(marsellus, mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).

?- loves(pumpkin,X), woman(X). no ?-
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Knowledge Base 5

• loves(vincent,mia).
• loves(marsellus,mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).
• jealous(X,Y)- loves(X,Z), loves(Y,Z).

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Knowledge Base 5

• loves(vincent,mia).
• loves(marsellus,mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).
• jealous(X,Y)- loves(X,Z), loves(Y,Z).

?- jealous(marsellus,W).
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Knowledge Base 5

• loves(vincent,mia).
• loves(marsellus,mia).
• loves(pumpkin, honey_bunny).
• loves(honey_bunny, pumpkin).
• jealous(X,Y)- loves(X,Z), loves(Y,Z).

?- jealous(marsellus,W). Wvincent ?-
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Prolog Syntax

• What exactly are facts, rules and queries built
  out of?

Terms
Terms
Simple Terms
Complex Terms
Simple Terms
Complex Terms
Constants
Variables
Constants
Variables
Atoms
Numbers
Atoms
Numbers
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Atoms

• A sequence of characters of upper-case letters,
  lower-case letters, digits, or underscore,
  starting with a lowercase letter
• Examples butch, big_kahuna_burger, playGuitar
• An arbitrary sequence of characters enclosed in
  single quotes
• Examples 'Vincent', 'Five dollar shake',
  '_at_'
• A sequence of special characters
• Examples , . -

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Numbers

• Integers 12, -34, 22342
• Floats 34573.3234

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Variables

• A sequence of characters of upper-case letters,
  lower-case letters, digits, or underscore,
  starting with either an uppercase letter or an
  underscore
• Examples X, Y, Variable, Vincent, _tag

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Complex Terms

• Atoms, numbers and variables are building blocks
  for complex terms
• Complex terms are built out of a functor directly
  followed by a sequence of arguments
• Arguments are put in round brackets, separated by
  commas
• The functor must be an atom

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Examples of complex terms

• Examples we have seen before
• playsAirGuitar(jody)
• loves(vincent, mia)
• jealous(marsellus, W)
• Complex terms inside complex terms
• hide(X,father(father(father(butch))))

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Arity

• The number of arguments a complex term has is
  called its arity
• Examples woman(mia) is a term with arity
  1 loves(vincent,mia) has arity 2
  father(father(butch)) arity 1

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Arity is important

• In Prolog you can define two predicates with the
  same functor but with different arity
• Prolog would treat this as two different
  predicates
• In Prolog documentation arity of a predicate is
  usually indicated with the suffix "/" followed by
  a number to indicate the arity

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Example of Arity
happy(yolanda). listens2music(mia). listens2music(
yolanda)- happy(yolanda). playsAirGuitar(mia)-
listens2music(mia). playsAirGuitar(yolanda)-
listens2music(yolanda).

• This knowledge base defines
• happy/1
• listens2music/1
• playsAirGuitar/1

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Summary of this lecture

• Simple examples of Prolog programs
• Introduced three basic constructs in Prolog
• Facts
• Rules
• Queries
• Discussed other concepts, such as
• the role of logic
• unification with the help of variables
• Definition of Prolog constructs terms, atoms,
  and variables

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Next Lecture?

• Discuss unification in Prolog
• Prolog's search strategy

75
Exercise Witches
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Example Family Tree
77
Example Sentence
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Example Crossword

• abalone
• abandon
• enhance
• anagram
• connect
• elegant

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Example Sudoku