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Figure 3. Completed tableau for (a Vv b) >a. form a contradiction. Similarly, node 3 is an ancestor of node 8 and when read conjunc- tively, trivially forms a contradiction. All branches are contradictory and closed, therefore the original formula is valid.

Figure 3 Completed tableau for (a Vv b) >a. form a contradiction. Similarly, node 3 is an ancestor of node 8 and when read conjunc- tively, trivially forms a contradiction. All branches are contradictory and closed, therefore the original formula is valid.

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Figure 2b. Tableau after the second step (applying Fi rule R1b on the second node). pplying Figure 2c. Completed tableau for ((a Vv b) A xa) =>b (reached after eight steps). A contradiction can be seen along the left-hand branch of the completed tableau: node 5 is an ancestor of node 6 so should be read conjunctively, however —a and a obviously
Figure 2b. Tableau after the second step (applying Fi rule R1b on the second node). pplying Figure 2c. Completed tableau for ((a Vv b) A xa) =>b (reached after eight steps). A contradiction can be seen along the left-hand branch of the completed tableau: node 5 is an ancestor of node 6 so should be read conjunctively, however —a and a obviously
Table 1. Basic tableaux rules. a recent surge in interest because of its applicability to modal logics, description logics and Semantic Web reasoning. A thorough overview of the method and applications to rea- soning with propositional, first order, modal, description and other logics can be found in D’ Agostino et al.’s (eds) handbook [11] or other standard references for formal computer science. For convenience, we present a brief review of the technique for the propositional case below.
Table 1. Basic tableaux rules. a recent surge in interest because of its applicability to modal logics, description logics and Semantic Web reasoning. A thorough overview of the method and applications to rea- soning with propositional, first order, modal, description and other logics can be found in D’ Agostino et al.’s (eds) handbook [11] or other standard references for formal computer science. For convenience, we present a brief review of the technique for the propositional case below.
Figure 6. Typical execution/interpretation process for a WorldSpace.
Figure 6. Typical execution/interpretation process for a WorldSpace.
Branch containing term: action = slow-move(x) Branch containing term: action = fast-move(x) Figure 7. Mid-action 3D rendering of the two tableau branches in the coffee cup action selection problem. In the right-hand branch we have a contradiction caused by the mess generated in th simulation and the mess constraint of our original query. The conclusion that our hybric ‘easoner draws is that the preferred action is to use the s/ow-move action on the cup o offee.
Branch containing term: action = slow-move(x) Branch containing term: action = fast-move(x) Figure 7. Mid-action 3D rendering of the two tableau branches in the coffee cup action selection problem. In the right-hand branch we have a contradiction caused by the mess generated in th simulation and the mess constraint of our original query. The conclusion that our hybric ‘easoner draws is that the preferred action is to use the s/ow-move action on the cup o offee.
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