PROLOG PROgramming in LOGic

Transcription

1 PROLOG PROgramming in LOGic 1 Knowledge Based Information Systems (Relational) database systems are very efficient in the handling of data. Information is data together with a suitable interpretation. Together with data (facts), knowledge based IS store interpretation rules. The information system can deduce additional data based on these rules. To express facts and rules, we use logic: Propositional Logic 1 : Propositions with a truth value and boolean operators. Predicate Logic 2 : Extends the propositional logic with variables, quantors and functions to describe rules. 1 Aussagenlogik 2 Prädikatenlogik c 2003 Jens Teubner, University of Konstanz 1

2 2 Implementation Idea: 1 Feed the information system with facts and rules. Use logic to describe them. 2 Ask questions concerning that knowledge: Can be yes or no questions, or the search for all variable bindings for which a given expression evaluates to true. PROLOG is an implementation of such a system. Prolog is not actually designed to work with large datasets. DATALOG is a variant to handle them. c 2003 Jens Teubner, University of Konstanz 2

3 Example: ➀ Feed facts:?- [user]. : cow(betty). : animal(x) :- cow(x). % betty is a cow (fact) % rule: cows are animals ➁ Pose queries:?- cow(betty). % is betty a cow? (query) Yes?- animal(betty). % is betty an animal? (query) Yes?- animal(x). % give me all animals X = betty ; % betty is a valid binding No % there are no more bindings c 2003 Jens Teubner, University of Konstanz 3

4 3 The Prolog Interpreter In the computer lab, the SWI-Prolog interpreter from the University of Amsterdam is installed. You can start it from the Linux command line: $ pl Welcome to SWI-Prolog (Version 5.0.1) Copyright (c) University of Amsterdam. SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software, and you are welcome to redistribute it under certain conditions. Please visit for details. For help, use?- help(topic). or?- apropos(word).?- You can exit the Prolog interpreter with ^D (Control-D) or by entering halt., followed by the enter key. c 2003 Jens Teubner, University of Konstanz 4

5 3.1 Finding Help in Prolog Prolog has an extensive online help utility. You can access it with the predicate help:?- help(consult). consult(+file) Read File as a Prolog source file. File may be a list of files, in which case all members are consulted in turn. [...] If you want to use Prolog at home, go to You can find sources or binaries for Linux, MacOS X and Windows. I can t give you support for this, however. c 2003 Jens Teubner, University of Konstanz 5

6 3.2 The Prolog Prompt Prolog can be in either one of the two operating modes query mode (Prompt?- or ) You can ask questions interactively in this mode. Prolog tries to give you an instance for the variables you specified that match your question or answers with Yes or No. consult mode (Prompt :) You can teach Prolog facts and rules in this mode. Rules are specified as Horn clauses. After startup, Prolog is in query mode. c 2003 Jens Teubner, University of Konstanz 6

7 3.2.1 Consult Mode Prolog is in consult mode while reading Prolog source files.?- [foo]. reads the file foo.pl in the current working directory. There is a special source file user. If you advise Prolog to read this file, the file is not read from your hard disk, but you can enter facts and rules on the Prolog prompt.?- [user]. : nice(weather). : ^D % user compiled 0.00 sec, 304 bytes Yes?- c 2003 Jens Teubner, University of Konstanz 7

8 4 Propositional Logic in Prolog 4.1 Facts Facts are represented in Prolog by identifiers that start with a lowercase letter, e. g. x. it_is_winter. i_like_prolog. Facts can be structured: is_bad(weather). owns(john, computer). research_group(professor(scholl), researchers(grust, seifert, teubner)). Don t put a space in front of the (. The structure can be arbitrarily deep. Predicates of this type can be interpreted as relations. Note that relations are distinguished by their name and their arity; relations with the same name but different number of parameters are completely distinct. In Prolog the closed world assumption holds: All facts you enter are true, everything else is considered false. c 2003 Jens Teubner, University of Konstanz 8

9 4.2 Rules Rules are facts that only hold under a certain prerequisite. In Prolog they are specified as which corresponds to the horn clause h :- g. g h g h Examples: z :- x. it_is_cold :- it_is_winter. is_nice(weather) :- not(is_bad(weather)). go_hiking :- is_nice(weather), have_time. will_lose(stuttgart) :- is_ill(hildebrand). Conjunctions are written as, in Prolog. Disjunctions are written as ;. c 2003 Jens Teubner, University of Konstanz 9

10 4.3 Queries After providing Prolog with a fact base, you can formulate queries on the knowledge represented by the given facts and rules. A query is formulated the same way as a fact. The system answers either Yes or No, depending on wether the query statement can be reduced to the facts and rules in the fact base. Prolog uses resolution to make its decision.?- it_is_cold. Yes.?- is_nice(weather). No. c 2003 Jens Teubner, University of Konstanz 10

11 5 Variables Variables in Prolog are identifiers that start with an uppercase letter, e. g. X, FOO, Student. In some cases, anonymous variables are helpful, written as an underscore ( ). 5.1 Variables in Queries Parts of a query can be replaced by a variable. The interpreter tries to find variable bindings that make the query statement true and prints them to the screen.?- animal(x). X = betty By typing a semicolon ( or? ) you can ask the system for more solutions. If no more are found, the system prints No. In queries the anonymous variable ( ) only asks for existence of a solution. If you use the anonymous variable more than once, they are distinct variables. c 2003 Jens Teubner, University of Konstanz 11

12 5.2 Variables in Rules Variables can be necessary in facts and rules to state correlations, either within a fact or between left and right side of the :-: : equal(x,x). : animal(x) :- cow(x). : sister(x,y) :- father(x,father), father(y,father), female(x), female(y). : likes(_, mary). The anonymous variable can be used as an every or don t care variable.?- [user]. : nice(weather(monday)). : not_nice(weather(tuesday)). : go_hiking(day) :- nice(weather(day)). : ^D % user compiled 0.00 sec, 828 bytes Yes?- go_hiking(monday). Yes?- go_hiking(tuesday). No?- c 2003 Jens Teubner, University of Konstanz 12

13 6 Prolog and Relational Databases When we told you about the Tuple Relational Calculus (TRC), you already heard something like the TRC is the 1st order predicate calculus. Prolog is an implementation of this calculus. Relations are predicates with as many parameters as the relation s attribute number. The database content is stored as facts. actor(1, Damon, Matt, male). actor(2, Potente, Franka, female). actor(3, Cruise, Tom, male). actor(4, Grant, Hugh, male). act_film(1, 3, Jason Bourne ). act_film(2, 3, Marie Kreutz ). The names of all actors? {t a : actor(a) t(name) = a(name)} actor(, Name, ). All actors with actor id smaller than 3? {t a : actor(a) t(actor id) < 3 t(actor id) = a(actor id) t(name) = a(name) t(sex) = a(sex)} actor(actor id, Name, Sex), Actor id < 3. c 2003 Jens Teubner, University of Konstanz 13

14 6.1 Joins and Views Joins are expressed like in the TRC: {t a, b : actor(a) act film(b) a(actor id) = b(actor id) t(name) = a(name) t(role) = b(role)} actor(id, Name, ), act film(id,, Role). Views in SQL correspond to rules in Prolog: CREATE VIEW actor_names AS SELECT Name From actor actor_names(name) :- actor(_, Name, _). c 2003 Jens Teubner, University of Konstanz 14

15 6.2 Recursive Queries With Prolog, it is also possible to express recursive queries. : son(otto, franz). : son(franz, heinz). : son(heinz, hugo). : descendant(d, A) :- son(d, A). : descendant(d, A) :- son(d, X), descendant(x, A).?- descendant(x, heinz). X = otto ; X = franz ; No?- c 2003 Jens Teubner, University of Konstanz 15