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This file is part of Logtalk https://logtalk.org/ SPDX-FileCopyrightText: 1998-2023 Paulo Moura <pmoura@logtalk.org> SPDX-License-Identifier: Apache-2.0

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

% start by loading the example:

| ?- logtalk_load(logic(loader)). ...

% translate a single logic proposition:

| ?- translator::translate((p v ~q) => (r & k), Cs). r :- p. k :- p. q; r :- . q; k :- .

Cs = [cl([r],[p]),cl([k],[p]),cl([q,r],[]),cl([q,k],[])] yes

% translate a single logic proposition printing each translation step:

| ?- translator::step_by_step((p v ~q) => (r & k), Cs).

Processing proposition: p v ~q=>r&k

1. Remove implications: ~ (p v ~q) v r&k
2. Distribute negation: ~p&q v r&k
3. Remove existential quantifiers: ~p&q v r&k
4. Convert to prenex normal form: ~p&q v r&k
5. Remove universal quantifiers: ~p&q v r&k
6. Convert to conjunctive normal form: (~p v r)&(~p v k)&((q v r)&(q v k))
7. Convert to clauses: [cl([r],[p]),cl([k],[p]),cl([q,r],[]),cl([q,k],[])]

Clauses in Prolog-like notation: r :- p. k :- p. q; r :- . q; k :- .

Cs = [cl([r],[p]),cl([k],[p]),cl([q,r],[]),cl([q,k],[])] yes

% translate a single logic proposition printing each translation step:

| ?- translator::step_by_step(all(X, exists(Y, p(X) v ~q(X) => r(X, Y))), Cs).

Processing proposition: all(X, exists(Y, p(X)v~q(X)=>r(X, Y)))

1. Remove implications: all(X, exists(Y, ~ (p(X)v~q(X))v r(X, Y)))
2. Distribute negation: all(X, exists(Y, ~p(X)&q(X)v r(X, Y)))
3. Remove existential quantifiers: all(X, ~p(X)&q(X)v r(X, f1(X)))
4. Convert to prenex normal form: all(X, ~p(X)&q(X)v r(X, f1(X)))
5. Remove universal quantifiers: ~p(X)&q(X)v r(X, f1(X))
6. Convert to conjunctive normal form: (~p(X)v r(X, f1(X)))& (q(X)v r(X, f1(X)))
7. Convert to clauses: [cl([r(X, f1(X))], [p(X)]), cl([q(X), r(X, f1(X))], [])]

Clauses in Prolog-like notation: r(X, f1(X)) :- p(X). q(X); r(X, f1(X)) :- .

X = X Y = f1(X) Cs = [cl([r(X, f1(X))], [p(X)]), cl([q(X), r(X, f1(X))], [])] yes

% translate a single logic proposition printing each translation step:

| ?- translator::step_by_step(all(X, men(X) => mortal(X)), Cs).

Processing proposition: all(X, men(X)=>mortal(X))

1. Remove implications: all(X, ~men(X)v mortal(X))
2. Distribute negation: all(X, ~men(X)v mortal(X))
3. Remove existential quantifiers: all(X, ~men(X)v mortal(X))
4. Convert to prenex normal form: all(X, ~men(X)v mortal(X))
5. Remove universal quantifiers: ~men(X)v mortal(X)
6. Convert to conjunctive normal form: ~men(X)v mortal(X)
7. Convert to clauses: [cl([mortal(X)], [men(X)])]

Clauses in Prolog-like notation: mortal(X) :- men(X).

X = X Cs = [cl([mortal(X)], [men(X)])] yes