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Logic Programming Peteris Erins

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p_e @

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Logic

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Logic Formal models of human reasoning

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Logic is expressive

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∀m ∃n ∀a ∀b (n ≥ m) ∧ [(a = 1) ∨ (b = 1) ∨ (ab ≠ n)] ?

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∀m ∃n ∀a ∀b (n ≥ m) ∧ [(a = 1) ∨ (b = 1) ∨ (ab ≠ n)] There are infinitely many primes ≡

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Prolog (1972)

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Relations are relationships between stuff

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human(you) less_than(2, 3) prefix(‘ban’, ‘banana’) even(X) relation name upper case for variables lower case for constants

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add(2, 3, 5) sorted([3, 1, 2], [1, 2, 3]) Functions are easily turned into relations add(2, 3) = 5

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Horn clauses

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Horn clauses If four legs and has a tail, then a dog many “if”s one “then”

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Horn clauses If four legs and has a tail, then a dog D is a dog if has four legs, has a tail

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Horn clauses If four legs and has a tail, then a dog D is a dog if has four legs, has a tail dog(D) if legs(D, 4) & has_tail(D)

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Horn clauses If four legs and has a tail, then a dog D is a dog if has four legs, has a tail dog(D) if legs(D, 4) & has_tail(D) dog(D) :- legs(D, 4), has_tail(D). “if” “and”

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Prolog, how does it work?

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even(2). even(4). even(6). Prolog, how does it work? 1. Write facts prolog, 2 is even prolog, 4 is even prolog, 6 is even

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even(2). even(4). even(6). Prolog, how does it work? 1. Write facts 2. Ask a question with a variable ?- even(X). prolog, 2 is even prolog, 4 is even prolog, 6 is even prolog, can you find an even X?

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even(2). even(4). even(6). Prolog, how does it work? 1. Write facts 2. Ask a question with a variable ?- even(X). 3. Prolog solves for the variable prolog, 2 is even prolog, 4 is even prolog, 6 is even prolog, can you find an even X? X = 2 ; X = 4 ; X = 6.

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Example Meta compiler? NLP grammar parser? Bayesian expert system?

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Example Meta compiler NLP grammar parser Bayesian expert system Todo list

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Todo list % source code file % [= fact/relation database] % interactive console for queries code repl

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Todo list code repl todo(Item) homework laundry dishes talk the relation we want to construct

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Todo list todo(homework). todo(laundry). todo(dishes). todo(talk). code repl todo(Item) homework laundry dishes talk the construction

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Todo list todo(homework). todo(laundry). todo(dishes). todo(talk). ?- todo(X). X = homework ; X = laundry ; X = dishes ; X = talk. code repl todo(Item) homework laundry dishes talk testing

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Todo list just_before(laundry, homework). just_before(dishes, laundry). ?- just_before(X, homework). X = laundry. code repl just_before just_before Before After laundry homework dishes laundry

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Todo list cannot_do(X) :- just_before(Y, X), todo(Y). ?- cannot_do(X). X = homework ; X = laundry. code repl cannot_do(Item) homework laundry

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Todo list code repl before before Before After laundry homework dishes laundry dishes homework just_before just_before Before After laundry homework dishes laundry

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Todo list before(X, Y) :- just_before(X, Y). before(X, Y) :- just_before(X, T), before(T, Y). ?- before(X, homework). X = laundry ; X = dishes. code repl before before Before After laundry homework dishes laundry dishes homework

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Todo list tag(homework, work). tag(laundry, home). tag(dishes, home). tag(talk, work). ?- tag(dishes, T). T = home. ?- tag(X, work). X = homework ; X = talk. code repl tag tag Task Tag homework work laundry home dishes home talk work

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Todo list agenda_tagged(Tag, Agenda) :- findall(X, tag(X, Tag) , Need_Doing), findall(X, cannot_do(X), Cant_Do), subtract(Need_Doing, Cant_Do, Agenda). ?- agenda_tagged(home,Y). Y = [dishes]. ?- agenda_tagged(work,Y). Y = [talk]. code repl agenda_tagged agenda_tagged Tag Agenda home [dishes] work [talk]

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How to think about logic programming?

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How to think about logic programming? 1. functional = imperative – mutable state logic = functional – manual search

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How to think about logic programming? 1. functional = imperative – mutable state logic = functional – manual search 2. combining database and program

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How to think about logic programming? 1. functional = imperative – mutable state logic = functional – manual search 2. combining database and program 3. an implementation of mathematical logic

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How to think about logic programming? 1. functional = imperative – mutable state logic = functional – manual search 2. combining database and program 3. an implementation of mathematical logic not really

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Here’s the catch: io flow scoping numerics

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Logic in the wild

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IBM Watson

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Wolfram Mathematica

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Datomic

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Type systems

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/** * Type class witnessing that `A` is less than or equal to `B`. * * @author Miles Sabin */ trait LTEq[A <: Nat, B <: Nat] object LTEq { import Nat._0 type <=[A <: Nat, B <: Nat] = LTEq[A, B] implicit def ltEq1 = new <=[_0, _0] {} implicit def ltEq2[B <: Nat] = new <=[_0, Succ[B]] {} implicit def ltEq3[A <: Nat, B <: Nat](implicit lt : A <= B) = new <=[Succ[A], Succ[B]] {} } Scala shapeless library Try finding the logic

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p_e @ Thank you! github.com/Pet3ris/talk-logic-programming Peteris Erins thanks to reviewers: @DARowlands @Sedols @Springcoil Panagiotis Charalampopolous special thanks: @swannodette @zoltanvarju @richlitt