.. _S4:

.. module:: pytableaux.logics.s4

**********************************
L{} - S4 Normal Modal Logic
**********************************

L{} is an extension of {@K} with a reflexive and transitive access relation.

.. contents::
    :local:
    :depth: 2

------------------------

.. _s4-semantics:

Semantics
=========

L{} semantics behave just like {@K semantics}.

Reflexivity
-----------

L{} includes the *reflexivity* restriction of {@T}:

.. include:: include/t/m.reflexivity.rst

Transitivity
------------

L{} adds an additional *transitivity* restriction:

.. include:: include/s4/m.transitivity.rst

.. _s4-system:

Tableaux
========

L{} tableaux are constructed just like {@K system} tableaux.

Nodes
-----

.. include:: include/k/nodes_blurb.rst

Trunk
-----

.. include:: include/k/trunk_blurb.rst

.. tableau::
  :build-trunk:
  :prolog:

Closure
-------

.. tableau-rules::
  :group: closure
  :docflags:
  :title: -

.. _s4-rules:

Rules
-----

L{} contains all the {@K rules}, the {@T} Reflexive rule, plus an
additional Transitive rule.

.. include:: include/s4/access_rules_group.rst

.. include:: include/k/rule_groups.rst

Notes
=====

References
==========

.. cssclass:: hidden

.. autoclass:: Rules()
  :members:
  :undoc-members: