The Tableau WorkBench (TWB) - Tableau
http://twb.rsise.anu.edu.au/taxonomy/term/35/0
enPropositional Modal Logic KD45
http://twb.rsise.anu.edu.au/propositional_modal_logic_kd45
<p>Also known as Weak S5 (WS5) because it lacks reflexivity, this logic is often used as the basis of logics of agents where []p means "the agent knows p" or "the agent believes p". </p>
<p>When you enter a formula A, then "closed" means that A is a theorem because the tableau for ~ A<br />
is closed, and "open" means that A is not a theorem because the tableau for ~ A is open.</p>
<p>Prover for modal logic KD45.<br />
Based on:<br />
Efficient Loop-Check for KD45 Logic<br />
A Birstunas<br />
Lithuanian Mathematics Journal 46(1):44-53 2006.</p>
<p>Author: Rajeev Gore 01 November 2007 (Copyright).</p>
<p><a href="http://twb.rsise.anu.edu.au/propositional_modal_logic_kd45">read more</a></p>TableauMon, 05 Nov 2007 10:20:49 +1100raj148 at http://twb.rsise.anu.edu.auPropositional Modal Logic KD
http://twb.rsise.anu.edu.au/modal_logic_kd
<p>KD extends basic normal modal logic K with the axiom<br />
D = []p -> <>p which forces the binary Kripke relation to be serial or total.<br />
That is, for every world w, there is a world v such that w R v holds.</p>
<p>KD is characterised by finite rooted trees where only the leaves have to be reflexive<br />
since all internal nodes have an R-successor.</p>
<p>When you enter a formula A, then "closed" means that A is a<br />
theorem because the tableau for ~ A is closed, and "open" means<br />
that it is not a theorem because the tableau for ~ A is open.</p>
TableauThu, 25 Oct 2007 03:15:10 +1000admin145 at http://twb.rsise.anu.edu.auPropositional Linear Temporal Logic PLTL
http://twb.rsise.anu.edu.au/pltl
<p>Propositional Linear Temporal Logic, also known as Propositional Linear Time Logic has the natural number<br />
line ordered by < as the intended model. It is used to model temporal behaviour with two basic modal<br />
operators X p interpreted as "the next state makes p true" and p Un q interpreted as "p is true from now<br />
until q becomes true". The other operators are defined from these.</p>
<p>When you enter a formula A, then "closed" means that A is a<br />
theorem because the tableau for ~ A is closed, and "open" means<br />
that it is not a theorem because the tableau for ~ A is open.</p>
TableauThu, 25 Oct 2007 03:09:54 +1000admin143 at http://twb.rsise.anu.edu.auPropositional Computational Tree Logic CTL
http://twb.rsise.anu.edu.au/ctl
<p>Often known as Branching Time Temporal Logic, CTL allows us to state properties which may be true<br />
on all paths or on some paths in a rooted tree where each branch is a copy of the natural numbers. </p>
<p>For an introduction to temporal logics, see<br />
<a href="http://plato.stanford.edu/entries/logic-temporal/" title="http://plato.stanford.edu/entries/logic-temporal/">http://plato.stanford.edu/entries/logic-temporal/</a></p>
<p>When you enter a formula A, then "closed" means that A is a<br />
theorem because the tableau for ~ A is closed, and "open" means<br />
that it is not a theorem because the tableau for ~ A is open.</p>
<p>When you enter a formula A, then "closed" means that A is a</p>
<p><a href="http://twb.rsise.anu.edu.au/ctl">read more</a></p>TableauThu, 25 Oct 2007 03:07:43 +1000admin142 at http://twb.rsise.anu.edu.auPropositional Dynamic Logic PDL (No UEV)
http://twb.rsise.anu.edu.au/pdlmarknouev
<p>This version of our prover is able to classify each branch as either closed or open at its leaf.<br />
Thus there is no need for the variable UEV which was used to identify Unfulfulled EVentualities<br />
and then was passed up from children to parents in our other tableau procedures PDL (UEV).</p>
<p>For an introduction to PDL see <a href="http://plato.stanford.edu/entries/logic-dynamic/" title="http://plato.stanford.edu/entries/logic-dynamic/">http://plato.stanford.edu/entries/logic-dynamic/</a></p>
<p>When you enter a formula A, then "closed" means that A is a<br />
theorem because the tableau for ~ A is closed, and "open" means<br />
that it is not a theorem because the tableau for ~ A is open.</p>
TableauThu, 25 Oct 2007 02:59:51 +1000admin141 at http://twb.rsise.anu.edu.auPropositional KLM Logic P
http://twb.rsise.anu.edu.au/klm
<p>This is a prover for KLM ( Kraus, Lehmann and Magidor ) logic P as defined in:<br />
L Gordano, V Gliozzi, N Olivetti, G Pozzato<br />
"Analytic tableaux for KLM Preferential and Cummulative Logic"<br />
Proceedings of LPAR 2005 LNAI 3835:666-681, Springer, 2005.</p>
<p>When you enter a formula A, then "closed" means that A is a<br />
theorem because the tableau for ~ A is closed, and "open" means<br />
that it is not a theorem because the tableau for ~ A is open.</p>
TableauTue, 23 Oct 2007 02:11:02 +1000admin139 at http://twb.rsise.anu.edu.auPropositional Modal Logic K4
http://twb.rsise.anu.edu.au/k4
<p>K4 has the following axion on top of normal modal logic K:<br />
[]p -> [][]p which enforces that the Kripke reachability relation R is transitive.</p>
<p>When you enter a formula A, then "closed" means that A is a<br />
theorem because the tableau for ~ A is closed, and "open" means<br />
that it is not a theorem because the tableau for ~ A is open.</p>
TableauTue, 23 Oct 2007 02:02:41 +1000admin138 at http://twb.rsise.anu.edu.auPropositional Modal Logic S4
http://twb.rsise.anu.edu.au/modal_logic_s4_0
<p>Also known as KT4 this logic add the following axioms to K:<br />
T = []p -> p which forces the Kripke reachability relation to be reflexive<br />
4 = []p -> [][]p which forces the Kripke reachability relation to be transitive.</p>
<p>It is characterised by finite rooted transitive trees of clusters where a cluster<br />
is a finite set of points with every world in the cluster reachable from every other world in the cluster. </p>
<p>When you enter a formula A, then "closed" means that A is a<br />
theorem because the tableau for ~ A is closed, and "open" means</p>
<p><a href="http://twb.rsise.anu.edu.au/modal_logic_s4_0">read more</a></p>TableauWed, 03 Oct 2007 04:08:36 +1000admin135 at http://twb.rsise.anu.edu.auPropositional Modal Logic K
http://twb.rsise.anu.edu.au/modal_logic_k_0
<p>The basic normal modal logic K is characterised by the set of all Kripke frames with a binary reachability<br />
relation. Its decision problem is PSPACE complete. </p>
<p>When you enter a formula A, then "closed" means that A is a<br />
theorem because the tableau for ~ A is closed, and "open" means<br />
that it is not a theorem because the tableau for ~ A is open.</p>
TableauWed, 03 Oct 2007 04:05:17 +1000admin134 at http://twb.rsise.anu.edu.auPropositional Dynamic Logic (SNF)
http://twb.rsise.anu.edu.au/propositional_dynamic_logic_snf
This version of PDL first transforms formulae into a *-normal form defined in the associated paper. The conversion to *-normal form can result in a blow up of the given formula e.g. < * * a > p gets converted to < (a ; *a) ; * (a ; *a) > p. Since this is suboptimal, there is another prover that does not require *-normal form. The rules of that prover are currently being written up.
When you enter a formula A, then "closed" means that A is a
theorem because the tableau for ~ A is closed, and "open" means
that it is not a theorem because the tableau for ~ A is open.
<p><a href="http://twb.rsise.anu.edu.au/propositional_dynamic_logic_snf">read more</a></p>TableauWed, 03 Oct 2007 03:37:49 +1000admin133 at http://twb.rsise.anu.edu.au