diff --git a/logic_programming/3_PropositionalLogic.ipynb b/logic_programming/3_PropositionalLogic.ipynb
index 1d7bf85f5f534d9fad82f9e2ca327008d2e24b3f..4566d56851b2b92faadc72b49c5b17b04a2c8871 100644
--- a/logic_programming/3_PropositionalLogic.ipynb
+++ b/logic_programming/3_PropositionalLogic.ipynb
@@ -366,10 +366,982 @@
"?- wff(Formula,\"(p∧(q∨(¬p)))\",\"\")."
]
},
+ {
+ "cell_type": "markdown",
+ "id": "f9005519",
+ "metadata": {},
+ "source": [
+ "The above Prolog term `and(p,or(q,not(p)))` represents the logical formula in tree form.\n",
+ "We can display the tree as a dag (directed acyclic graph) using the following subsidiary code\n",
+ "(in future the Jupyter kernel will probably have a dedicated command to show a term graphically):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "f6116612",
+ "metadata": {
+ "vscode": {
+ "languageId": "prolog"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <style>\n",
+ " details {\n",
+ " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
+ " }\n",
+ "\n",
+ " details > summary {\n",
+ " cursor: pointer;\n",
+ " }\n",
+ " </style>\n",
+ " <details><summary>Previously defined clauses of user:subtree/3 were retracted (click to expand)</summary><pre>:- dynamic subtree/3.\n",
+ "\n",
+ "subtree(A, B, C) :-\n",
+ " A=..[_|D],\n",
+ " nth1(B, D, C).\n",
+ "</pre></details>"
+ ],
+ "text/plain": [
+ "Previously defined clauses of user:subtree/3 were retracted:\n",
+ ":- dynamic subtree/3.\n",
+ "\n",
+ "subtree(A, B, C) :-\n",
+ " A=..[_|D],\n",
+ " nth1(B, D, C).\n"
+ ]
+ },
+ "metadata": {
+ "application/json": {}
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "% Asserting clauses for user:subtree/3\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <style>\n",
+ " details {\n",
+ " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
+ " }\n",
+ "\n",
+ " details > summary {\n",
+ " cursor: pointer;\n",
+ " }\n",
+ " </style>\n",
+ " <details><summary>Previously defined clauses of user:rec_subtree/2 were retracted (click to expand)</summary><pre>:- dynamic rec_subtree/2.\n",
+ "\n",
+ "rec_subtree(A, B) :-\n",
+ " A=B.\n",
+ "rec_subtree(A, B) :-\n",
+ " subtree(A, _, C),\n",
+ " rec_subtree(C, B).\n",
+ "</pre></details>"
+ ],
+ "text/plain": [
+ "Previously defined clauses of user:rec_subtree/2 were retracted:\n",
+ ":- dynamic rec_subtree/2.\n",
+ "\n",
+ "rec_subtree(A, B) :-\n",
+ " A=B.\n",
+ "rec_subtree(A, B) :-\n",
+ " subtree(A, _, C),\n",
+ " rec_subtree(C, B).\n"
+ ]
+ },
+ "metadata": {
+ "application/json": {}
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "% Asserting clauses for user:rec_subtree/2\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <style>\n",
+ " details {\n",
+ " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
+ " }\n",
+ "\n",
+ " details > summary {\n",
+ " cursor: pointer;\n",
+ " }\n",
+ " </style>\n",
+ " <details><summary>Previously defined clauses of user:subnode/3 were retracted (click to expand)</summary><pre>:- dynamic subnode/3.\n",
+ "\n",
+ "subnode(A, [shape/B, label/C], D) :-\n",
+ " rec_subtree(D, A),\n",
+ " functor(A, C, _),\n",
+ " ( atom(A)\n",
+ " -> B=egg\n",
+ " ; number(A)\n",
+ " -> B=oval\n",
+ " ; B=rect\n",
+ " ).\n",
+ "</pre></details>"
+ ],
+ "text/plain": [
+ "Previously defined clauses of user:subnode/3 were retracted:\n",
+ ":- dynamic subnode/3.\n",
+ "\n",
+ "subnode(A, [shape/B, label/C], D) :-\n",
+ " rec_subtree(D, A),\n",
+ " functor(A, C, _),\n",
+ " ( atom(A)\n",
+ " -> B=egg\n",
+ " ; number(A)\n",
+ " -> B=oval\n",
+ " ; B=rect\n",
+ " ).\n"
+ ]
+ },
+ "metadata": {
+ "application/json": {}
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "% Asserting clauses for user:subnode/3\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "subtree(Term,Nr,SubTerm) :- \n",
+ " Term =.. [_|ArgList], %obtain arguments of the term\n",
+ " nth1(Nr,ArgList,SubTerm). % get sub-argument and its position number\n",
+ "\n",
+ "% recursive and transitive closure of subtree\n",
+ "rec_subtree(Term,Sub) :- Term = Sub.\n",
+ "rec_subtree(Term,Sub) :- subtree(Term,_,X), rec_subtree(X,Sub).\n",
+ "\n",
+ "subnode(Sub,[shape/S, label/F],Formula) :- \n",
+ " rec_subtree(Formula,Sub), % any sub-formula Sub of Formula is a node in the graphical rendering\n",
+ " functor(Sub,F,_), (atom(Sub) -> S=egg ; number(Sub) -> S=oval ; S=rect)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "d7e68593",
+ "metadata": {
+ "vscode": {
+ "languageId": "prolog"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "Node | Dot | \n",
+ ":- | :- | \n",
+ "and(p,or(q,not(p))) | [shape/rect,label/and] | \n",
+ "p | [shape/egg,label/p] | \n",
+ "or(q,not(p)) | [shape/rect,label/or] | \n",
+ "q | [shape/egg,label/q] | \n",
+ "not(p) | [shape/rect,label/not] | \n",
+ "p | [shape/egg,label/p] | "
+ ],
+ "text/plain": [
+ "Node | Dot | \n",
+ ":- | :- | \n",
+ "and(p,or(q,not(p))) | [shape/rect,label/and] | \n",
+ "p | [shape/egg,label/p] | \n",
+ "or(q,not(p)) | [shape/rect,label/or] | \n",
+ "q | [shape/egg,label/q] | \n",
+ "not(p) | [shape/rect,label/not] | \n",
+ "p | [shape/egg,label/p] | "
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[1mtrue"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "jupyter:print_table(subnode(Node,Dot,and(p,or(q,not(p)))))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "3646e3ee",
+ "metadata": {
+ "vscode": {
+ "languageId": "prolog"
+ }
+ },
+ "outputs": [
+ {
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+ "text/plain": [
+ "digraph {\n",
+ "\"p\" [shape=\"egg\", label=\"p\"]\n",
+ "\"q\" [shape=\"egg\", label=\"q\"]\n",
+ "\"not(p)\" [shape=\"rect\", label=\"not\"]\n",
+ "\"and(p,or(q,not(p)))\" [shape=\"rect\", label=\"and\"]\n",
+ "\"or(q,not(p))\" [shape=\"rect\", label=\"or\"]\n",
+ " \"not(p)\" -> \"p\" [label=\"1\", color=\"black\", style=\"solid\"]\n",
+ " \"and(p,or(q,not(p)))\" -> \"p\" [label=\"1\", color=\"black\", style=\"solid\"]\n",
+ " \"and(p,or(q,not(p)))\" -> \"or(q,not(p))\" [label=\"2\", color=\"black\", style=\"solid\"]\n",
+ " \"or(q,not(p))\" -> \"q\" [label=\"1\", color=\"black\", style=\"solid\"]\n",
+ " \"or(q,not(p))\" -> \"not(p)\" [label=\"2\", color=\"black\", style=\"solid\"]\n",
+ "}"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[1mtrue"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "jupyter:show_graph(subnode(_,_,and(p,or(q,not(p)))),subtree/3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "11b3a8ad",
+ "metadata": {},
+ "source": [
+ "Below we will study how one can assign a truth-value to logical formulas like the one above.\n",
+ "\n",
+ "## Truth tables\n",
+ "\n",
+ "Every logical connective has a truth-table, indicating how it maps the truth of its arguments to its own truth value.\n",
+ "For example, `and` maps inputs `true` and `false` to `false`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "id": "350b9756",
+ "metadata": {
+ "vscode": {
+ "languageId": "prolog"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <style>\n",
+ " details {\n",
+ " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
+ " }\n",
+ "\n",
+ " details > summary {\n",
+ " cursor: pointer;\n",
+ " }\n",
+ " </style>\n",
+ " <details><summary>Previously defined clauses of user:not/2 were retracted (click to expand)</summary><pre>:- dynamic not/2.\n",
+ "\n",
+ "not(true, false).\n",
+ "not(false, true).\n",
+ "</pre></details>"
+ ],
+ "text/plain": [
+ "Previously defined clauses of user:not/2 were retracted:\n",
+ ":- dynamic not/2.\n",
+ "\n",
+ "not(true, false).\n",
+ "not(false, true).\n"
+ ]
+ },
+ "metadata": {
+ "application/json": {}
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "% Asserting clauses for user:not/2\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <style>\n",
+ " details {\n",
+ " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
+ " }\n",
+ "\n",
+ " details > summary {\n",
+ " cursor: pointer;\n",
+ " }\n",
+ " </style>\n",
+ " <details><summary>Previously defined clauses of user:and/3 were retracted (click to expand)</summary><pre>:- dynamic and/3.\n",
+ "\n",
+ "and(true, A, A).\n",
+ "and(false, _, false).\n",
+ "</pre></details>"
+ ],
+ "text/plain": [
+ "Previously defined clauses of user:and/3 were retracted:\n",
+ ":- dynamic and/3.\n",
+ "\n",
+ "and(true, A, A).\n",
+ "and(false, _, false).\n"
+ ]
+ },
+ "metadata": {
+ "application/json": {}
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "% Asserting clauses for user:and/3\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <style>\n",
+ " details {\n",
+ " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
+ " }\n",
+ "\n",
+ " details > summary {\n",
+ " cursor: pointer;\n",
+ " }\n",
+ " </style>\n",
+ " <details><summary>Previously defined clauses of user:or/3 were retracted (click to expand)</summary><pre>:- dynamic or/3.\n",
+ "\n",
+ "or(true, _, true).\n",
+ "or(false, A, A).\n",
+ "</pre></details>"
+ ],
+ "text/plain": [
+ "Previously defined clauses of user:or/3 were retracted:\n",
+ ":- dynamic or/3.\n",
+ "\n",
+ "or(true, _, true).\n",
+ "or(false, A, A).\n"
+ ]
+ },
+ "metadata": {
+ "application/json": {}
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "% Asserting clauses for user:or/3\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
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+ "data": {
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+ "\n",
+ " <style>\n",
+ " details {\n",
+ " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
+ " }\n",
+ "\n",
+ " details > summary {\n",
+ " cursor: pointer;\n",
+ " }\n",
+ " </style>\n",
+ " <details><summary>Previously defined clauses of user:implies/3 were retracted (click to expand)</summary><pre>:- dynamic implies/3.\n",
+ "\n",
+ "implies(A, B, C) :-\n",
+ " not(A, D),\n",
+ " or(D, B, C).\n",
+ "</pre></details>"
+ ],
+ "text/plain": [
+ "Previously defined clauses of user:implies/3 were retracted:\n",
+ ":- dynamic implies/3.\n",
+ "\n",
+ "implies(A, B, C) :-\n",
+ " not(A, D),\n",
+ " or(D, B, C).\n"
+ ]
+ },
+ "metadata": {
+ "application/json": {}
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "% Asserting clauses for user:implies/3\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
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+ "data": {
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+ " details {\n",
+ " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
+ " }\n",
+ "\n",
+ " details > summary {\n",
+ " cursor: pointer;\n",
+ " }\n",
+ " </style>\n",
+ " <details><summary>Previously defined clauses of user:equiv/3 were retracted (click to expand)</summary><pre>:- dynamic equiv/3.\n",
+ "\n",
+ "equiv(A, B, C) :-\n",
+ " implies(A, B, D),\n",
+ " implies(B, A, E),\n",
+ " and(D, E, C).\n",
+ "</pre></details>"
+ ],
+ "text/plain": [
+ "Previously defined clauses of user:equiv/3 were retracted:\n",
+ ":- dynamic equiv/3.\n",
+ "\n",
+ "equiv(A, B, C) :-\n",
+ " implies(A, B, D),\n",
+ " implies(B, A, E),\n",
+ " and(D, E, C).\n"
+ ]
+ },
+ "metadata": {
+ "application/json": {}
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "% Asserting clauses for user:equiv/3\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <style>\n",
+ " details {\n",
+ " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
+ " }\n",
+ "\n",
+ " details > summary {\n",
+ " cursor: pointer;\n",
+ " }\n",
+ " </style>\n",
+ " <details><summary>Previously defined clauses of user:truth_value/1 were retracted (click to expand)</summary><pre>:- dynamic truth_value/1.\n",
+ "\n",
+ "truth_value(true).\n",
+ "truth_value(false).\n",
+ "</pre></details>"
+ ],
+ "text/plain": [
+ "Previously defined clauses of user:truth_value/1 were retracted:\n",
+ ":- dynamic truth_value/1.\n",
+ "\n",
+ "truth_value(true).\n",
+ "truth_value(false).\n"
+ ]
+ },
+ "metadata": {
+ "application/json": {}
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "% Asserting clauses for user:truth_value/1\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <style>\n",
+ " details {\n",
+ " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
+ " }\n",
+ "\n",
+ " details > summary {\n",
+ " cursor: pointer;\n",
+ " }\n",
+ " </style>\n",
+ " <details><summary>Previously defined clauses of user:truth_table/7 were retracted (click to expand)</summary><pre>:- dynamic truth_table/7.\n",
+ "\n",
+ "truth_table(A, B, C, D, E, F, G) :-\n",
+ " truth_value(A),\n",
+ " truth_value(B),\n",
+ " not(A, C),\n",
+ " and(A, B, D),\n",
+ " or(A, B, E),\n",
+ " implies(A, B, F),\n",
+ " equiv(A, B, G).\n",
+ "</pre></details>"
+ ],
+ "text/plain": [
+ "Previously defined clauses of user:truth_table/7 were retracted:\n",
+ ":- dynamic truth_table/7.\n",
+ "\n",
+ "truth_table(A, B, C, D, E, F, G) :-\n",
+ " truth_value(A),\n",
+ " truth_value(B),\n",
+ " not(A, C),\n",
+ " and(A, B, D),\n",
+ " or(A, B, E),\n",
+ " implies(A, B, F),\n",
+ " equiv(A, B, G).\n"
+ ]
+ },
+ "metadata": {
+ "application/json": {}
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "% Asserting clauses for user:truth_table/7\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "not(true,false).\n",
+ "not(false,true).\n",
+ "\n",
+ "and(true,V,V) :- truth_value(V).\n",
+ "and(false,_,false).\n",
+ "\n",
+ "or(true,_,true).\n",
+ "or(false,V,V) :- truth_value(V).\n",
+ "\n",
+ "implies(A,B,Res) :- not(A,NotA), or(NotA,B,Res).\n",
+ "equiv(A,B,Res) :- implies(A,B,AiB), implies(B,A,BiA), and(AiB,BiA,Res).\n",
+ "\n",
+ "truth_value(true).\n",
+ "truth_value(false).\n",
+ "\n",
+ "truth_table(A,B,NotA,AandB,AorB,AiB,AeB) :- \n",
+ " truth_value(A), truth_value(B),\n",
+ " not(A,NotA), and(A,B,AandB), or(A,B,AorB),\n",
+ " implies(A,B,AiB), equiv(A,B,AeB)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "id": "54b57ff8",
+ "metadata": {
+ "vscode": {
+ "languageId": "prolog"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "A | B | NotA | AandB | AorB | AimpliesB | AequivB | \n",
+ ":- | :- | :- | :- | :- | :- | :- | \n",
+ "true | true | false | true | true | true | true | \n",
+ "true | false | false | false | true | false | false | \n",
+ "false | true | true | false | true | true | false | \n",
+ "false | false | true | false | false | true | true | "
+ ],
+ "text/plain": [
+ "A | B | NotA | AandB | AorB | AimpliesB | AequivB | \n",
+ ":- | :- | :- | :- | :- | :- | :- | \n",
+ "true | true | false | true | true | true | true | \n",
+ "true | false | false | false | true | false | false | \n",
+ "false | true | true | false | true | true | false | \n",
+ "false | false | true | false | false | true | true | "
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[1mtrue"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "jupyter:print_table(truth_table(A,B,NotA,AandB,AorB,AimpliesB,AequivB))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "id": "175c00d0",
+ "metadata": {
+ "vscode": {
+ "languageId": "prolog"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <style>\n",
+ " details {\n",
+ " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
+ " }\n",
+ "\n",
+ " details > summary {\n",
+ " cursor: pointer;\n",
+ " }\n",
+ " </style>\n",
+ " <details><summary>Previously defined clauses of user:value/3 were retracted (click to expand)</summary><pre>:- dynamic value/3.\n",
+ "\n",
+ "value(A, B, C) :-\n",
+ " atomic(A),\n",
+ " member(A/C, B).\n",
+ "value(and(A, B), C, D) :-\n",
+ " value(A, C, E),\n",
+ " value(B, C, F),\n",
+ " and(E, F, D).\n",
+ "value(or(A, B), C, D) :-\n",
+ " value(A, C, E),\n",
+ " value(B, C, F),\n",
+ " or(E, F, D).\n",
+ "value(not(A), B, C) :-\n",
+ " value(A, B, D),\n",
+ " not(D, C).\n",
+ "value(implies(A, B), C, D) :-\n",
+ " value(or(not(A), B), C, D).\n",
+ "value(equiv(A, B), C, D) :-\n",
+ " value(and(implies(A, B), implies(B, A)),\n",
+ " C,\n",
+ " D).\n",
+ "</pre></details>"
+ ],
+ "text/plain": [
+ "Previously defined clauses of user:value/3 were retracted:\n",
+ ":- dynamic value/3.\n",
+ "\n",
+ "value(A, B, C) :-\n",
+ " atomic(A),\n",
+ " member(A/C, B).\n",
+ "value(and(A, B), C, D) :-\n",
+ " value(A, C, E),\n",
+ " value(B, C, F),\n",
+ " and(E, F, D).\n",
+ "value(or(A, B), C, D) :-\n",
+ " value(A, C, E),\n",
+ " value(B, C, F),\n",
+ " or(E, F, D).\n",
+ "value(not(A), B, C) :-\n",
+ " value(A, B, D),\n",
+ " not(D, C).\n",
+ "value(implies(A, B), C, D) :-\n",
+ " value(or(not(A), B), C, D).\n",
+ "value(equiv(A, B), C, D) :-\n",
+ " value(and(implies(A, B), implies(B, A)),\n",
+ " C,\n",
+ " D).\n"
+ ]
+ },
+ "metadata": {
+ "application/json": {}
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "% Asserting clauses for user:value/3\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "value(X,Interpretation,Value) :- \n",
+ " atomic(X), % we could also use: proposition(X),\n",
+ " member(X/Value,Interpretation).\n",
+ "value(and(A,B),I,Val) :- value(A,I,VA), value(B,I,VB),\n",
+ " and(VA,VB,Val).\n",
+ "value(or(A,B),I,Val) :- value(A,I,VA), value(B,I,VB),\n",
+ " or(VA,VB,Val).\n",
+ "value(not(A),I,Val) :- value(A,I,VA),\n",
+ " not(VA,Val).\n",
+ "value(implies(A,B),I,Val) :- value(or(not(A),B),I,Val).\n",
+ "value(equiv(A,B),I,Val) :- \n",
+ " value(and(implies(A,B),implies(B,A)),I,Val).\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "id": "eee17774",
+ "metadata": {
+ "vscode": {
+ "languageId": "prolog"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[1mRes = false"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "?- value(and(p,or(q,not(p))), [p/true, q/false],Res)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "id": "78473da0",
+ "metadata": {
+ "vscode": {
+ "languageId": "prolog"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "P | Q | Res | \n",
+ ":- | :- | :- | \n",
+ "true | true | true | \n",
+ "true | false | false | \n",
+ "false | true | false | \n",
+ "false | false | false | "
+ ],
+ "text/plain": [
+ "P | Q | Res | \n",
+ ":- | :- | :- | \n",
+ "true | true | true | \n",
+ "true | false | false | \n",
+ "false | true | false | \n",
+ "false | false | false | "
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[1mtrue"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "jupyter:print_table(value(and(p,or(q,not(p))), [p/P, q/Q],Res))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "id": "2ee60c15",
+ "metadata": {
+ "vscode": {
+ "languageId": "prolog"
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <style>\n",
+ " details {\n",
+ " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
+ " }\n",
+ "\n",
+ " details > summary {\n",
+ " cursor: pointer;\n",
+ " }\n",
+ " </style>\n",
+ " <details><summary>Previously defined clauses of user:subnode_val/4 were retracted (click to expand)</summary><pre>:- dynamic subnode_val/4.\n",
+ "\n",
+ "subnode_val(A, [shape/B, label/C, style/filled, fillcolor/D], E, F) :-\n",
+ " rec_subtree(E, A),\n",
+ " functor(A, C, _),\n",
+ " ( atom(A)\n",
+ " -> B=egg\n",
+ " ; number(A)\n",
+ " -> B=oval\n",
+ " ; B=rect\n",
+ " ),\n",
+ " ( value(A, F, true)\n",
+ " -> D=olive\n",
+ " ; D=salmon1\n",
+ " ).\n",
+ "</pre></details>"
+ ],
+ "text/plain": [
+ "Previously defined clauses of user:subnode_val/4 were retracted:\n",
+ ":- dynamic subnode_val/4.\n",
+ "\n",
+ "subnode_val(A, [shape/B, label/C, style/filled, fillcolor/D], E, F) :-\n",
+ " rec_subtree(E, A),\n",
+ " functor(A, C, _),\n",
+ " ( atom(A)\n",
+ " -> B=egg\n",
+ " ; number(A)\n",
+ " -> B=oval\n",
+ " ; B=rect\n",
+ " ),\n",
+ " ( value(A, F, true)\n",
+ " -> D=olive\n",
+ " ; D=salmon1\n",
+ " ).\n"
+ ]
+ },
+ "metadata": {
+ "application/json": {}
+ },
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "% Asserting clauses for user:subnode_val/4\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "\n",
+ "subnode_val(Sub,[shape/S, label/F, style/filled, fillcolor/C],Formula,Interpretation) :- \n",
+ " rec_subtree(Formula,Sub), % any sub-formula Sub of Formula is a node in the graphical rendering\n",
+ " functor(Sub,F,_), (atom(Sub) -> S=egg ; number(Sub) -> S=oval ; S=rect),\n",
+ " (value(Sub,Interpretation,true) -> C=olive ; C=sienna1)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "id": "2b497dad",
+ "metadata": {
+ "vscode": {
+ "languageId": "prolog"
+ }
+ },
+ "outputs": [
+ {
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+ "text/plain": [
+ "digraph {\n",
+ "\"p\" [shape=\"egg\", label=\"p\", style=\"filled\", fillcolor=\"olive\"]\n",
+ "\"q\" [shape=\"egg\", label=\"q\", style=\"filled\", fillcolor=\"sienna1\"]\n",
+ "\"not(p)\" [shape=\"rect\", label=\"not\", style=\"filled\", fillcolor=\"sienna1\"]\n",
+ "\"and(p,or(q,not(p)))\" [shape=\"rect\", label=\"and\", style=\"filled\", fillcolor=\"sienna1\"]\n",
+ "\"or(q,not(p))\" [shape=\"rect\", label=\"or\", style=\"filled\", fillcolor=\"sienna1\"]\n",
+ " \"not(p)\" -> \"p\" [label=\"1\", color=\"black\", style=\"solid\"]\n",
+ " \"and(p,or(q,not(p)))\" -> \"p\" [label=\"1\", color=\"black\", style=\"solid\"]\n",
+ " \"and(p,or(q,not(p)))\" -> \"or(q,not(p))\" [label=\"2\", color=\"black\", style=\"solid\"]\n",
+ " \"or(q,not(p))\" -> \"q\" [label=\"1\", color=\"black\", style=\"solid\"]\n",
+ " \"or(q,not(p))\" -> \"not(p)\" [label=\"2\", color=\"black\", style=\"solid\"]\n",
+ "}"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[1mtrue"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "jupyter:show_graph(subnode_val(_,_,and(p,or(q,not(p))),[p/true,q/false]),subtree/3)"
+ ]
+ },
{
"cell_type": "code",
"execution_count": null,
- "id": "f6116612",
+ "id": "0fd23f05",
"metadata": {
"vscode": {
"languageId": "prolog"