Logic and Programs Most programs use Boolean expressions

Logic and Programs • Most programs use Boolean expressions over data • Logic statements can express program semantics – I. e. , axiomatic semantics • Logic also can be the subject of computation – E. g. , automatic deduction systems, theorem-provers • Can handle computation and proof interchangeably – E. g. , for restricted forms of logic (Horn Clauses FOL) • Programming languages then can help automate this – E. g. , logic programming in Prolog • Mechanisms readily implemented in a functional style – E. g. , in Scheme or other functional programming languages CSE 425: Logic Programming I

Logic Programs • Logic programming languages (and programming frameworks in other languages like Scheme or C++) – Provide a means for encoding well formed statements – Provide algorithms for implementing inference rules • Sometimes called “deductive databases” – Logic programming systems as logic + control where the logic is specified and the control is automated – To be feasible, however, some restrictions are needed • Widely applicable beyond theorem proving – E. g. , programming robots to adapt to situational factors CSE 425: Logic Programming I

Intro to Prolog • The most widely used logic programming language – Though lots of logic programming is done in other languages • Syntax is similar to first-order-logic (FOL) syntax – E. g. , ancestor(x, y)^ancestor(y, z) → ancestor(x, z) in FOL is ancestor(X, Z) : - ancestor(X, Y), ancestor(Y, Z) in Prolog – Note: variables are capitalized (or begin with an underscore) – Note: comma indicates conjunction (and) – Also, Prolog uses =< instead of <= for less-than-or equal • Lists are delimited by square brackets in Prolog – E. g. , [alice, bob, X] • Can do head|tail matching (as in ML, Haskell) – E. g. , [H|T] = [alice, bob, X] gives [alice] and [bob, X] CSE 425: Logic Programming I

Prolog Interpreter Environment • Maintains a database of statements and variables – E. g. , loaded from a file, and/or entered by the user • User can enter a predicate as a query – – E. g. , ancestor(bob, alice) Interpreter matches query to statements in its database If query is fully bound, will produce a yes or no answer If query has a variable, will find a satisfactory binding • User also can ask for the result of an expression – E. g. , X is 3 + 5, write(X) • Unification in Prolog – A constant only unifies with itself (exact match is required), while a variable may unify via renaming and/or binding – Predicates unify if same signature, and the arguments unify CSE 425: Logic Programming I

Today’s Studio Exercises • We’ll code up initial ideas from Scott Chapter 11 – Looking at basic parsing and evaluation mechanisms for propositional and predicate logic, and proceeding from there • Today’s exercises are again in C++ – Please take advantage of the text books and the on-line pages that are linked on the course web site – As always, please ask for help as needed • When done, e-mail your answers to the cse 425@seas. wustl. edu course account, with subject line “Logic Programming Studio I” CSE 425: Logic Programming I