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json.html
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json.html
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<!DOCTYPE html>
<html lang="en">
<head itemscope>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="description" content="Online logic solvers.">
<meta name="author" content="Tanel Tammet">
<meta name="keywords" content="logic, solvers, reasoning, propositions, dpll, resolution, truth table">
<meta itemprop="itemtype" content="http://schema.org/SoftwareApplication">
<meta itemprop="name" content="Logictools">
<meta itemprop="description" content="Logic solvers and conversion tools.">
<meta itemprop="url" content="http://logictools.org">
<meta itemprop="operatingSystems" content="Linux, Windows">
<meta itemprop="softwareApplicationCategory" content="WebApplication">
<meta property="og:title" content="Logictools">
<meta property="og:url" content="http://logictools.org">
<meta property="og:site_name" content="Logictools">
<meta property="og:type" content="website">
<meta property="og:description" content="Logic solvers and conversion tools.">
<meta property="fb:admins" content="tanel.tammet">
<link rel="shortcut icon" href="logo.png">
<title>Logictools</title>
<!-- Bootstrap core CSS -->
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/css/bootstrap.min.css">
<!-- Custom styles for this template -->
<link rel="stylesheet" href="https://fonts.googleapis.com/css2?family=Roboto+Mono&family=Inconsolata&family=Roboto:wght@300&display=swap">
<link rel="stylesheet" href="wdb.css">
<style>
html.wf-loading * {
opacity: 0;
}
.result {
padding: 15px;
white-space: pre-wrap;
}
.intro {
padding: 15px;
}
.nice-container {
border: 1;
border-width: 1px, 1px, 1px, 1px;
border-radius: 5px;
color: #666;
}
.result_wiblock {
padding: 0px;
color: black;
font-family: 'Inconsolata','Roboto Mono','Courier New', Courier, monospace;
border-width: 1px, 1px, 1px, 1px;
border-radius: 5px;
}
.intro_wiblock {
padding: 0px;
color: #333;
}
.syntax {
width: 70px; height: 30px; text-align: center;
padding: 0px 0px 1px 0px; font-size: 12px;
line-height: 1.42; border-radius: 15px;
background-color: #cccccc; color: #337ab7; margin-left: 15px;
}
.btn-prove {
font-family: Arial, Helvetica, sans-serif;
}
/*
.btn-convert {
background-color: #337ab7;
}
*/
.btn-file {
position: relative;
overflow: hidden;
}
.btn-file input[type=file] {
position: absolute;
top: 0;
right: 0;
min-width: 100px;
min-height: 100px;
font-size: 100%;
text-align: right;
filter: alpha(opacity=0);
opacity: 0;
outline: none;
background: white;
cursor: inherit;
display: block;
}
code {
padding: .1em .4em;
margin: 2px 5px 2px 5px;
font-size: 100%;
color:black !important;
background-color: #f4f4f4 !important;
border-radius: 4px;
font-family: 'Inconsolata','Roboto Mono','Courier New', Courier, monospace;
}
pre {
background-color: white !important;
}
pre code {
padding: 0 !important;
margin: 0 !important;
font-size: 100% !important;
color: #222 !important;
background-color: white !important;
border-radius: 0 !important;
}
</style>
<script src="https://ajax.googleapis.com/ajax/libs/webfont/1.6.26/webfont.js"></script>
<script>
WebFont.load({
google: {
families: ['Roboto', 'Inconsolata']
}
});
</script>
<script>
'use strict';
var gkcoutput="";
function useGkc(el) {
var el, placeid;
var input, output, textflag;
var inputarea, outputplace;
var arglist;
var sel, conversion, print_level, print_derived, strategy, seconds;
el=document.getElementById("intro");
el.innerHTML="";
var placeid=el.parentNode.id;
var div = document.getElementById(placeid+"_output");
//clearOutputByPlace(placeid);
inputarea=document.getElementById("gkc_1_input");
outputplace=document.getElementById("result");
input=inputarea.value;
if (seemsJson(input)) textflag="-jstext";
else textflag="-text"
sel=document.getElementById("format_select");
conversion=sel.options[sel.selectedIndex].value;
if (conversion=="json" || conversion=="tptp") {
arglist=[textflag,input,"-"+conversion];
} else if (conversion=="simple" || conversion=="clauses") {
arglist=[textflag,input];
} else {
conversion=conversion.substring(8);
arglist=[textflag,input,"-"+conversion];
}
sel=document.getElementById("print_level");
print_level=sel.options[sel.selectedIndex].value;
arglist=arglist.concat(['-print',print_level]);
sel=document.getElementById("print_derived");
print_derived=sel.options[sel.selectedIndex].value;
if (print_derived=="on") {
arglist=arglist.concat(['-derived']);
}
sel=document.getElementById("strategy");
strategy=sel.value;
if (strategy) {
arglist=arglist.concat(['-strategytext',strategy]);
}
sel=document.getElementById("seconds");
seconds=sel.value;
if (seconds) {
seconds=parseInt(seconds);
if (isNaN(seconds)) seconds=5;
arglist=arglist.concat(['-seconds',""+seconds]);
} else {
arglist=arglist.concat(['-seconds',"5"]);
}
arglist=arglist.concat(['-parallel',"0"]);
//console.log(arglist);
gkcoutput="";
gkc(arglist);
//console.log("gkcoutput",gkcoutput);
document.getElementById("result").innerHTML=gkcoutput.trim();
}
function seemsJson(str) {
var c, len;
var i,lpar=0,rpar=0,lbrack=0,lcurl=0,rcurl=0,rbrack=0,quotes=0,periods=0,perc=0;
var tptpsymbs=0, jssymbs=0;
if (!str) return 0;
len=str.length;
for(i=0; i<len; i++) {
c=str[i];
if (c=='[') lbrack++;
else if (c==']') rbrack++;
else if (c=='{') lcurl++;
else if (c=='}') rcurl++;
else if (c=='(') lpar++;
else if (c==')') rpar++;
else if (c=='"') quotes++;
else if (c=='.') periods++;
else if (c=='%') perc++;
}
//console.log(lbrack,lcurl,rbrack,rcurl,quotes,periods);
if (!lbrack && !lcurl) return 0;
if (!rbrack && !rcurl) return 0;
if (!quotes) return 0;
if (!periods && quotes) return 1;
tptpsymbs=2*lpar+2*rpar+periods+perc;
jssymbs=lbrack+rbrack+2*lcurl+2*rcurl+2*quotes;
//console.log(jssymbs,tptpsymbs);
if (jssymbs>tptpsymbs) return 1;
else return 0;
}
function gkc(arglist) {
Module.callMain(arglist);
}
function convert(el) {
var el,placeid;
var input, output, textflag;
var inputarea, outputplace;
var arglist;
var conversion;
var sel;
el=document.getElementById("intro");
el.innerHTML="";
var placeid=el.parentNode.id;
var div = document.getElementById(placeid+"_output");
//clearOutputByPlace(placeid);
inputarea=document.getElementById("gkc_1_input");
outputplace=document.getElementById("result");
input=inputarea.value;
if (seemsJson(input)) textflag="-jstext";
else textflag="-text"
sel=document.getElementById("conversion_select");
conversion=sel.options[sel.selectedIndex].value;
if (conversion=="json" || conversion=="tptp") {
arglist=[textflag,input,"-convert","-"+conversion];
} else if (conversion=="simple" || conversion=="clauses") {
arglist=[textflag,input,"-clausify"];
} else {
conversion=conversion.substring(8);
arglist=[textflag,input,"-clausify","-"+conversion];
}
gkcoutput="";
//console.log(arglist);
gkc(arglist);
//console.log("gkcoutput",gkcoutput);
document.getElementById("result").innerHTML=gkcoutput;
}
function clearOutputByPlace(placeid) {
var div = document.getElementById(placeid+"_output");
while(div.firstChild){
div.removeChild(div.firstChild);
}
}
function clearOutput(el) {
document.getElementById("result").innerHTML="";
document.getElementById("proof_notes").innerHTML="";
}
/*
function clearInputByPlace(placeid) {
document.getElementById(placeid+"_input").value="";
}
*/
function clearInput(el) {
var sel;
sel=document.getElementById("select_example");
if (sel) sel.options.selectedIndex=0;
document.getElementById("gkc_1_input").value="";
document.getElementById("input_notes").innerHTML="";
}
function fillOutput(placeid,text) {
document.getElementById(placeid+"_output").innerHTML=text;
}
// example selection
function selectExample(level) {
var sel;
var value;
var data;
var notes;
var placeid,html,el;
el=document.getElementById("intro");
el.innerHTML="";
if (level=='simple') sel=document.getElementById("select_example");
else sel=document.getElementById("select_advanced_example");
value=sel.options[sel.selectedIndex].value;
if (value=="examples") {
document.getElementById("input_notes").innerHTML="";
document.getElementById("proof_notes").innerHTML="";
document.getElementById("result").innerHTML="";
return;
}
placeid="example_"+value+"_";
el=document.getElementById(placeid+"input_code");
if (el) {
html=el.innerHTML;
if (html) {
html=html.replace(new RegExp("&","g"),"&");
html=html.replace(new RegExp(">","g"),">");
html=html.replace(new RegExp("<","g"),"<");
document.getElementById("gkc_1_input").value=html;
}
}
if (!el || !html) document.getElementById("gkc_1_input").value="";
el=document.getElementById(placeid+"input_notes");
if (el) {
html=el.innerHTML;
if (html) {
document.getElementById("input_notes").innerHTML=html;
}
}
if (!el || !html) document.getElementById("input_notes").innerHTML="";
el=document.getElementById(placeid+"proof_notes");
if (el) {
html=el.innerHTML;
if (html) {
document.getElementById("proof_notes").innerHTML=html;
}
}
if (!el || !html) document.getElementById("proof_notes").innerHTML="";
html="<div class='click_prove'>Click the Prove button!</div>";
html="<button onclick='useGkc(this); return false;' ";
html+="class='btn btn-small btn-primary btn-prove'style='width: 70px;''>Prove</button>";
document.getElementById("result").innerHTML=html;
}
function switchAdvanced() {
if ($('#advanced_buttons').is(":hidden")) {
//$('#ctf_show_configuremenu').val('1');
//$('#configure_btn').attr('value',clstr[2]);
} else {
//$('#ctf_show_configuremenu').val('0');
//$('#configure_btn').attr('value',clstr[1]);
}
$('#advanced_buttons').slideToggle('slow');
};
// simplified Module glue code originally produced by emscripten
var Module={
noInitialRun: true,
preRun:[],
postRun:[],
print: function(s) {
gkcoutput+=s+"\n";
},
printErr:function(e){
arguments.length>1 && (e=Array.prototype.slice.call(arguments).join(" "));
if ((JSON.stringify(e)).includes("abort(OOM)")) {
location.reload();
} else if ((JSON.stringify(e)).includes("index out of bounds")) {
location.reload();
} else if ((JSON.stringify(e)).includes("timeout")) {
location.reload();
}
console.error(e);
},
setStatus:function(e){ return 1 },
totalDependencies:0,
monitorRunDependencies:function(e){
this.totalDependencies=0;
Module.setStatus(e ? "Preparing... ("+(this.totalDependencies-e)+"/"+this.totalDependencies+")"
: "All downloads complete.")
}
};
/*
window.onerror=function(e){
console.error(e);
// Module.setStatus("Exception thrown, see JavaScript console"),
// Module.setStatus=function(e){
// e && Module.printErr("[post-exception status] "+e)
// }
}
*/
</script>
</head>
<body>
<div id="fb-root"></div>
<div class="navbar navbar-inverse navbar-static-top" style="background-color: #333333;">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-collapse">
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a class="navbar-brand" href="index.html">Logictools</a>
</div>
<div class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li class="dummy"><a href="index.html">Predicate logic</a></li>
<li class="dummy"><a href="prop.html">Propositional logic</a></li>
<li class="active"><a href="json.html">Json</a></li>
<!-- <li class="dummy"><a href="predicate.html">Predicate logic</a></li> -->
<li class="dummy"><a href="download.html">Download</a></li>
<li class="dummy"><a href="about.html">About</a></li>
</ul>
</div><!--/.navbar-collapse -->
</div>
</div>
<!-- content after titlebar -->
<div class="container">
<div class="row">
<div class="col-md-12 wblock wblock1">
<!--------------------------- --->
<h2 style="font-family: 'Roboto',Arial,Helvetica,sans-serif; font-weight: 300; line-height: 1.1;">Solve JSON and JSON-LD examples:
<button type="button" class="btn btn-default"
onclick="gid('syntax').style.display='block'; document.location='#syntax'; "
style="
width: 70px; height: 30px; text-align: center;
padding: 0px 0px 1px 0px; font-size: 12px;
line-height: 1.42; border-radius: 15px;
background-color: #cccccc; color: #337ab7; margin-left: 15px;"
>help</button>
</h2>
<div class="form-inline" method="post" osnubmit="return false;">
<div class="wblock">
<div id="gkc_1">
<textarea class="form-control" id="gkc_1_input" spellcheck="false"
style="height: 200px; width:100%; margin-bottom: 20px; color: black;
font-family: 'Inconsolata','Roboto Mono','Courier New', Courier, monospace; ">[ // a simple example: find a grandson of john
["father","john","pete"],
["father","pete","mark"],
["forall", ["X","Y","Z"], [[["father","X","Y"], "&", ["father","Y","Z"]], "=>", ["grandfather","X","Z"]]],
["forall", ["X"], [["grandfather","john","X"],"=>",["$ans","X"]]]
]</textarea>
<button onclick="useGkc(this); return false;" class="btn btn-small btn-primary btn-prove"
style="width: 70px;">Prove</button>
<!-- <div style="display: inline-block; width: 50px; text-align: center;">simple</div> -->
<select class="form-control" style="width: 180px;" id="select_example"
onchange="selectExample('simple')">
<option value="examples">examples</option>
<option value="1">json basics</option>
<option value="2">more connectives</option>
<option value="3">answers</option>
<option value="4">free variables</option>
<option value="5">equality</option>
<option value="6">gf with equality</option>
<option value="7">json-ld basics</option>
<option value="8">json maps in logic</option>
<option value="9">json-ld context</option>
<option value="10">nested maps and arithmetic</option>
<option value="11">named graphs and quads</option>
<option value="12">the list datatype</option>
<option value="13">distinct symbols</option>
</select>
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Read, prove and modify <a href="https://en.wikipedia.org/wiki/JSON">JSON</a> syntax examples
for predicate logic as defined in the
<a href="https://github.com/tammet/json-ld-logic">JSON-LD-LOGIC</a> proposal
with the following goals:
<p>
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<p>Providing a simple format for the programmatic management, parsing and printing of logical problems and proofs.
<br>Compatibility with the <a href="http://tptp.org">TPTP</a> language used by
most high-end full FOL reasoners, as described in the
<a href="http://tptp.org/TPTP/TR/TPTPTR.shtml#ProblemPresentation">TPTP technical manual</a>.
<br>Compatibility with <a href="https://json-ld.org/">JSON-LD</a>,
see the <a href="https://www.w3.org/TR/json-ld11/">W3C recommendation</a>.
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<p>
A playground for the proposed
<a href="https://github.com/tammet/json-ld-logic">JSON-LD-LOGIC</a> syntax for
<a href="https://en.wikipedia.org/wiki/First-order_logic">first order predicate logic</a>
formulas: proving, answering questions
and converting between different syntaxes for logic.
<p>
The JSON-LD-LOGIC syntax has the following goals:
<ul>
<li>Providing a simple format for the programmatic management,
parsing and printing of logical problems and proofs.
<li>Compatibility with the TPTP language used by most high-end full FOL reasoners,
as described in the
<a href="http://tptp.org/TPTP/TR/TPTPTR.shtml#ProblemPresentation">TPTP technical manual</a>.
<li>Compatibility with
<a href="https://json-ld.org/">JSON-LD</a>, see the
<a href="https://www.w3.org/TR/json-ld11/">W3C recommendation</a>.
</ul>
<p>
The toolkit is built around a high-performance reasoner
<a href="https://github.com/tammet/gkc">gkc</a> (see
<a href="https://link.springer.com/chapter/10.1007%2F978-3-030-29436-6_32">the paper</a>)
and runs in the browser using
<a href="https://en.wikipedia.org/wiki/WebAssembly">Wasm</a> without any server
involvement. For more advanced use you may want to
download the command-line version.
<p>
Use it for learning logic and experimenting with a reasoner.
<p>
Note: the gkc implementation allows the use of both line comments <code>//</code> and
multi-line comments <code>/* ...: */</code> in JSON.
<p>
For more details about logic and automated reasoning, have a look at the
<i>help</i> text of the <a href="index.html">Predicate logic</a> page
and go through the explanations in the <i>simple examples</i> selection
there.
<p>
The examples on the current page illustrate the JSON-LD-LOGIC syntax,
its conversion to
<a href="http://tptp.org/TPTP/TR/TPTPTR.shtml#ProblemPresentation">TPTP format</a>
and other specifics. It is recommended to go through these sequentially in
a tutorial-like manner.
<p>
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<p>
This is a playground for the proposed
<a href="https://github.com/tammet/json-ld-logic">JSON-LD-LOGIC</a> syntax for logic, with the
following goals:
<ul>
<li>Providing a simple format for the programmatic management,
parsing and printing of logical problems and proofs.
<li>Compatibility with the TPTP language used by most high-end full FOL reasoners,
as described in the
<a href="http://tptp.org/TPTP/TR/TPTPTR.shtml#ProblemPresentation">TPTP technical manual</a>.
<li>Compatibility with
<a href="https://json-ld.org/">JSON-LD</a>, see the
<a href="https://www.w3.org/TR/json-ld11/">W3C recommendation</a>.
</ul>
<p>
Basic use: pick a problem from the two boxes of examples, read the explanations and
press <i>Prove</i>. You can select your own problem files, edit or modify examples
directly in the text area of the browser. The prover runs in your browser using
Wasm as as a single process. The proofs are also presented in JSON by default.
<p>
If you are new to this, it is helpful to first try out and read the problems
sequentially from the <i>simple examples</i> of the
<a href="index.html">Predicate logic</a>, organized as a tutorial. The
<i>help</i> text there is also useful.
<p>
The underlying machinery on the current page is exactly the same as on the
<a href="index.html">Predicate logic</a> page.
<p>
Press the <i>Advanced</i> button for selecting the options such as time limit (default
5 seconds), detail level of the proof and proof format. You can also select and compose
your own search strategies.
<p>
The <i>Convert to</i> button does not attempt to prove a formula,
but converts it to the selected format. The <i>... clauses</i> formats convert the
formula to the
<a href="https://en.wikipedia.org/wiki/Conjunctive_normal_form">clause</a> or conjunctive
normal form actually used for search. The default <i>simple format</i> is explained in the
<i>help</i>
text of the <a href="index.html">Predicate logic</a> menu,
the tptp format is a de facto standard format for most high-end provers (see the
<a href="http://tptp.org/TPTP/TR/TPTPTR.shtml#ProblemPresentation">TPTP technical manual</a>)
and the json format follows the proposed
<a href="https://github.com/tammet/json-ld-logic">JSON-LD-LOGIC</a> syntax.
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You can set the time limit in seconds. Beware that for long-running search processes the
browser may regularly propose to stop the script. The prover selects a number (typically
ca 30) different search strategies and tries out these sequentially, repeating the process
with the incrementally growing time limits. These <i>internal</i> time limits start
at 0.1 seconds for one search attempt.
<p>
You can increase the print level to gain more information about what is going
on during the search, automatically selected search strategies and statistics. In particular,
selecting <i>Show derived: on</i> will cause the prover to print out all the derived clauses after
the search has successfully stopped. Beware: the amount can be enormous.
<p>
You can also enter your own search strategies and settings instead of using the automatically
generated ones: please have a look at the <i>complex: strategy</i> example under
<a href="index.html">Predicate logic</a> page for details. For modern provers the search strategy
selection typically dominates over all the other considerations and optimizations.
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<div hidden>
<div id="example_1_input_notes"><h3>Example 1 for json basics</h3>
<p>This is a simple example for the basics of the json syntax for predicate logic
as presented in the <a href="https://github.com/tammet/json-ld-logic">JSON-LD-LOGIC</a>
specification.
Later examples will show other features of the json syntax like functions, equality,
json-ld syntax conversion, lists, arithmetics, unique symbols and such.</p>
<p>For the introductory examples of logic and automated reasoning without the use or
focus on the JSON syntax you may want to check the <i>Solve predicate logic</i> top menu.
<p>Here we first have two facts in the json syntax where predicates (names of relations)
are the first element of a list: <code>["father","john","pete"]</code> means
<i>john is the father of pete</i>. We then have a grandfather rule using a quantifier <code>"forall"</code>
for three variables (use only strings with the capital first letter for variables),
<code>"&"</code> meaning "and", <code>"=>"</code> meaning "implies".
</p>
<p>
We will ask whether from these
two facts and a rule we can derive that there exists somebody who has <i>john</i> as a grandfather: the
last formula is a negation of this question, using <code>"not"</code> with the obvious meaning.
The whole list of statements is treated as a conjunction (<i>and</i>) of all statements.
</p>
<p>Why the negation and contradiction? This is just a convenient way to simplify
the problem. Suppose we want to prove <code>a & b => a</code>. This is true
if and only if <code>-(a & b => a)</code> is false. Now, the last formula
is equivalent to <code>a & b & -a</code>. Thus
the input facts and rules stay as they are, and we only negate the conclusion to be proved.
To summarize, giving a goal to be proved from axioms (i.e. known facts / rules) as a negated
statement is just a convenient way to organize proof search and there is nothing really
special about it.</p>
</div>
<p>Although comments are not allowed in standard json, gkc accepts both line
comments <code>//</code> and multi-line comments <code>/* .... */</code> in json.
</p>
<p>The order of statements in the list is not really important, although it may cause minor
and essentially unpredictable differences in search behaviour. Essentially, gkc
creates and tries out its own search strategies, like SQL databases. It does not
follow a pre-determined predictable search strategy like PROLOG.</p>
<p>Input file example1.txt:</p>
<pre><code id="example_1_input_code">[
["father","john","pete"],
["father","pete","mark"],
["forall", ["X","Y","Z"], [[["father","X","Y"], "&", ["father","Y","Z"]], "=>", ["grandfather","X","Z"]]],
// negated question: does there exist somebody who has john as a grandfather?
["forall", ["X"], ["not",["grandfather","john","X"]]]
]
</code></pre>
<div id="example_1_proof_notes">
<p>The output is a json object with two keys:
<ul>
<li> <code>result</code> indicates whether the proof was found,
<li> <code>answers</code> contains a list of all answers and proofs for these answers.
Here we did not ask to find a concrete person, so we have only
a single answer containing just a <code>proof</code> key indicating a list with the
numbered steps of the proof found: each step is either a used input fact / rule or a
derived fact / rule.</p>
</ul>
<p>The formulas in the proof are always just lists of atoms (called <i>clauses</i>)
treated as a disjunction (<i>or</i>).
<p>Observe that
<ul>
<li><code>["-father","?:X","pete"]</code> means the same as <code>["not" ["father","?:X","pete"]]</code>.
<li>Strings prefixed by <code>?:</code> like <code>?:X</code> are <i>free variables</i>
implicitly assumed to be quantified by "forall".
</ul>
<p><code>["in","frm_N" ]</code> means that the clause stems from the fact/rule number
<i>N</i> given as input.</p>
<p><code>["mp", 1, 2]</code> means that this <i>clause</i>
was derived by modus ponens (i.e. the
<a href="https://en.wikipedia.org/wiki/Resolution_(logic)">resolution rule</a>)
from previous steps 1 and 2. More concretely, the first literals of both were cut off and
the rest were glued together. <code>["mp", 3, 4, 5]</code> means that the clause was first
derived from clauses 3 and 4 and then the clause 5 was used for and additional
simplifying resolution step.</p>
<p>The <a href="https://en.wikipedia.org/wiki/Resolution_(logic)">Resolution (logic) wiki page</a>
is a good short intro to the general principles of the derivation rules with the
<a href="http://lambda.ee/w/images/0/06/Geoffreasoningnotes.pdf">course materials of Geoff Sutcliffe</a>
being a suitable continuation towards deeper understanding. However,
our examples are understandable without in-depth theoretical background.</p>
<p>Try to modify the example by removing the statement <code>["father","john","pete"],</code> and
run the gkc prover again. After ca one second gkc will stop and output</p>
<pre><code>{"result": "proof not found"}</code></pre>
<p>Although the task is trivial, gkc does not attempt to be clever and tries out a large number
of search strategies: this is why it takes a second to terminate. You can click on <i>Advanced</i> and
select <i>Print level</i> value <i>+ runs</i> or any later option in the select list to see the whole process:
later options will give huge amounts of output.</p>
<p>In case gkc does not understand the syntax of the input file it will give a json-formatted
error typically indicating a culprit line and piece of input like this:</p>
<pre><code>{"error": "syntax error, unexpected URI, expecting '.': file example1.txt place 'as' in line 3:
foo bar ("}</code></pre> or <pre><code>{"error": "json syntax error: lexical error: invalid char in json text.
"}</code></pre>
You may also want to <b>convert</b> the example to some other language by clicking on
the <i>Convert to</i> button: first select an output language from the box after the button before
conversion.</div>
<div id="example_2_input_notes"><h3>Example 2 for more connectives</h3>
We use the equivalence <code>"<=>"</code>, disjunction <code>"|"</code>
and <code>"not"</code> connectives for a slightly more
complicated family example, this time defining the
grandfather predicate as either a paternal or maternal grandfather.
You can use <code>"not"</code>, <code>"~"</code> or <code>"-"</code>
for logical negation <i>not</i>: they have the same meaning.
The tilde <code>~</code> and minus <code>-</code> characters can be used as a prefix of a
symbol to denote negation: the last line could be equivalently written as
<code>["forall", ["X"], ["-grandfather","john","X"]]</code>.
</div>
<pre>
<code id="example_2_input_code">[
["father","john","eve"],
["mother","eve","mark"],
["forall", ["X","Y","Z"], [
[[["father","X","Y"], "&", ["father","Y","Z"]],
"|",
[["father","X","Y"], "&", ["mother","Y","Z"]]],
"<=>",
["grandfather","X","Z"]]
],
["forall", ["X"], ["not",["grandfather","john","X"]]]
]
</code>
</pre>
<div id="example_2_proof_notes">
</div>
<div id="example_3_input_notes"><h3>Example 3 for answers</h3>
<p>Like example 1, but we want to find a concrete person as an answer: we use the special
<code>"$ans"</code> predicate for this. Deriving a clause containing only atoms with the
<code>"$ans"</code> predicate means that the proof has been found.
</div>
<pre><code id="example_3_input_code">[
["father","john","pete"],
["father","pete","mark"],
["forall", ["X","Y","Z"], [[["father","X","Y"], "&", ["father","Y","Z"]], "=>", ["grandfather","X","Z"]]],
["forall", ["X"], [["grandfather","john","X"],"=>",["$ans","X"]]]
]
</code></pre>
<div id="example_3_proof_notes">
<p>Notice that gkc output contains a key <code>"answer": [["$ans","mark"]],</code>
indicating the substitution made for <code>X</code>: <i>mark</i> is the answer we were looking for.</p>
<p>Modify the example and try out the line</p>
<pre><code>["forall", ["X","Y"], [["grandfather","Y","X"],"=>",["$ans","Y","X"]]]
</code></pre>
<p>You will get <code> [["$ans","john","mark"]]</code> in the output.
</div>
<div id="example_4_input_notes"><h3>Example 4 for free variables and syntactic sugar</h3>
<p>
Strings prefixed by <code>?:</code> like <code>"?:X"</code> are <i>free variables</i>
implicitly assumed to be quantified by <i>forall</i>.
</p>
<p>
The <code>["if" ... "then" ....]</code> construction is a convenient syntax instead
of implication: a list of formulas before <code>"then"</code> is treated
as a conjunction premiss of the implication and the list after
<code>"then"</code> as a disjunction consequent of the implication. For example,
<code>["if", "a", "b", "c", "then", "d", "e"]</code> is translated as
<code>[["a","&","b","&","c"], "=>", ["d","|","e"]]</code>.
</p>
<p>
The <code>"<="</code> connective stands for implication from right to left.
The full list of infix binary connectives follows the TPTP language:
<ul>
<li><code>"|"</code> for disjunction,
<li><code>"&"</code> for conjunction,
<li><code>"<=>"</code> for equivalence,
<li><code>"=>"</code> for implication,
<li><code>"<="</code> for reverse implication,