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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · SoleLogics.jl</title><script data-outdated-warner src="assets/warner.js"></script><link rel="canonical" href="https://aclai-lab.github.io/SoleLogics.jl/"/><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>SoleLogics.jl</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#Introduction"><span>Introduction</span></a></li><li><a class="tocitem" href="#Installation"><span>Installation</span></a></li><li><a class="tocitem" href="#Feature-Summary"><span>Feature Summary</span></a></li></ul></li><li><a class="tocitem" href="getting-started/">Getting started</a></li><li><a class="tocitem" href="propositional-logic/">Propositional logic</a></li><li><a class="tocitem" href="modal-logic/">Modal logic</a></li><li><a class="tocitem" href="autodocs/">Full reference</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/aclai-lab/SoleLogics.jl/blob/main/docs/src/index.md#" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="SoleLogics"><a class="docs-heading-anchor" href="#SoleLogics">SoleLogics</a><a id="SoleLogics-1"></a><a class="docs-heading-anchor-permalink" href="#SoleLogics" title="Permalink"></a></h1><h2 id="Introduction"><a class="docs-heading-anchor" href="#Introduction">Introduction</a><a id="Introduction-1"></a><a class="docs-heading-anchor-permalink" href="#Introduction" title="Permalink"></a></h2><p>Welcome to the documentation for <a href="https://github.com/aclai-lab/SoleLogics.jl">SoleLogics</a>, a Julia package for <a href="https://en.wikipedia.org/wiki/Computational_logic">computational logic</a>. SoleLogics.jl lays the logical foundations for <a href="https://github.com/aclai-lab/Sole.jl">Sole.jl</a>, an open-source framework for symbolic machine learning.</p><h2 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h2><p>To install SoleLogics.jl, use the Julia package manager:</p><pre><code class="language-julia hljs">using Pkg
Pkg.add(&quot;SoleLogics&quot;)</code></pre><h2 id="Feature-Summary"><a class="docs-heading-anchor" href="#Feature-Summary">Feature Summary</a><a id="Feature-Summary-1"></a><a class="docs-heading-anchor-permalink" href="#Feature-Summary" title="Permalink"></a></h2><p>SoleLogics.jl allows easy manipulation of:</p><ul><li>Syntax tokens (e.g., atoms, logical constants/connectives, etc.);</li><li>Alphabets, grammars, algebras (e.g., crisp, fuzzy), logics (e.g., propositional and (multi)modal);</li><li><a href="https://en.wikipedia.org/wiki/Well-formed_formula">Formulas</a> (e.g., syntax trees, DNFs, CNFs): random generation, parsing, minimization;</li><li><a href="https://en.wikipedia.org/wiki/Interpretation_(logic)">Interpretations</a> (e.g., propositional assignments, <a href="https://en.wikipedia.org/wiki/Kripke_structure_(model_checking)">Kripke structures</a>);</li><li>Algorithms for evaluating the: validity/satisfiability of a formula, and truth of a formula on an interpretation (<a href="https://en.wikipedia.org/wiki/Model_checking">model checking</a>).</li></ul></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="getting-started/">Getting started »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 8 November 2023 10:05">Wednesday 8 November 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
Pkg.add(&quot;SoleLogics&quot;)</code></pre><h2 id="Feature-Summary"><a class="docs-heading-anchor" href="#Feature-Summary">Feature Summary</a><a id="Feature-Summary-1"></a><a class="docs-heading-anchor-permalink" href="#Feature-Summary" title="Permalink"></a></h2><p>SoleLogics.jl allows easy manipulation of:</p><ul><li>Syntax tokens (e.g., atoms, logical constants/connectives, etc.);</li><li>Alphabets, grammars, algebras (e.g., crisp, fuzzy), logics (e.g., propositional and (multi)modal);</li><li><a href="https://en.wikipedia.org/wiki/Well-formed_formula">Formulas</a> (e.g., syntax trees, DNFs, CNFs): random generation, parsing, minimization;</li><li><a href="https://en.wikipedia.org/wiki/Interpretation_(logic)">Interpretations</a> (e.g., propositional assignments, <a href="https://en.wikipedia.org/wiki/Kripke_structure_(model_checking)">Kripke structures</a>);</li><li>Algorithms for evaluating the: validity/satisfiability of a formula, and truth of a formula on an interpretation (<a href="https://en.wikipedia.org/wiki/Model_checking">model checking</a>).</li></ul></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="getting-started/">Getting started »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 8 November 2023 10:29">Wednesday 8 November 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Modal logic · SoleLogics.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link rel="canonical" href="https://aclai-lab.github.io/SoleLogics.jl/modal-logic/"/><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">SoleLogics.jl</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../getting-started/">Getting started</a></li><li><a class="tocitem" href="../propositional-logic/">Propositional logic</a></li><li class="is-active"><a class="tocitem" href>Modal logic</a></li><li><a class="tocitem" href="../autodocs/">Full reference</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Modal logic</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Modal logic</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/aclai-lab/SoleLogics.jl/blob/main/docs/src/modal-logic.md#" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><ul><li><a href="#modal-logic">Modal Logic</a></li></ul><h1 id="modal-logic"><a class="docs-heading-anchor" href="#modal-logic">Modal Logic</a><a id="modal-logic-1"></a><a class="docs-heading-anchor-permalink" href="#modal-logic" title="Permalink"></a></h1></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../propositional-logic/">« Propositional logic</a><a class="docs-footer-nextpage" href="../autodocs/">Full reference »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 8 November 2023 10:05">Wednesday 8 November 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Modal logic · SoleLogics.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link rel="canonical" href="https://aclai-lab.github.io/SoleLogics.jl/modal-logic/"/><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">SoleLogics.jl</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../getting-started/">Getting started</a></li><li><a class="tocitem" href="../propositional-logic/">Propositional logic</a></li><li class="is-active"><a class="tocitem" href>Modal logic</a></li><li><a class="tocitem" href="../autodocs/">Full reference</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Modal logic</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Modal logic</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/aclai-lab/SoleLogics.jl/blob/main/docs/src/modal-logic.md#" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><ul><li><a href="#modal-logic">Modal Logic</a></li></ul><h1 id="modal-logic"><a class="docs-heading-anchor" href="#modal-logic">Modal Logic</a><a id="modal-logic-1"></a><a class="docs-heading-anchor-permalink" href="#modal-logic" title="Permalink"></a></h1></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../propositional-logic/">« Propositional logic</a><a class="docs-footer-nextpage" href="../autodocs/">Full reference »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 8 November 2023 10:29">Wednesday 8 November 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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