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Research Articles

Qualitative spatial reasoning with uncertain evidence using Markov logic networks

Matt Duckhama School of Science, RMIT University, Melbourne, AustraliaCorrespondence[email protected]

https://orcid.org/0000-0002-7249-6709 View further author information

Jelena Gabelab Department of Geodesy and Geoinformation, TU Wien, Vienna, Austria

https://orcid.org/0000-0002-0186-5917 View further author information

Allison Kealyc Surveying and Spatial, Victorian Department of Transport and Planning, Melbourne, Australia

https://orcid.org/0000-0002-6776-3411 View further author information

Ross Kyprianoud Defence Science and Technology, Australian Government, Edinburgh, Australia

https://orcid.org/0000-0002-8873-4417 View further author information

Jonathan Leggd Defence Science and Technology, Australian Government, Edinburgh, AustraliaView further author information

Bill Morane Defence Technologies, The University of Melbourne, Melbourne, Australia

https://orcid.org/0000-0001-6219-2341 View further author information

Shakila Khan Rumif Specialist Capabilities Unit, Australian Institute of Health and Welfare (AIHW), Canberra, Australia

https://orcid.org/0000-0002-8927-597X View further author information

Flora D. Salimg School of Computer Science & Engineering, University of New South Wales (UNSW), NSW, Australia

https://orcid.org/0000-0002-1237-1664 View further author information

Yaguang Taoa School of Science, RMIT University, Melbourne, Australia

https://orcid.org/0000-0002-6335-1452 View further author information

Maria Vasardanih Data and Analytics, Aurecon Group Pty Ltd, Melbourne, Australia

https://orcid.org/0000-0003-0208-0561 View further author information

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Figures & data

Figure 1. An example ground Markov random field for east–west calculus.

Figure 2. Example direction relations between relatum O₁ and locata O₂, F₁ and F₂.

Figure 2. Example direction relations between relatum O1 and locata O2, F1 and F2.

Figure 3. Results of experiment E1 with soft evidence SE1 $dir (O_{2}, O_{1}, SE)$ with scenarios S1–3 with probabilities 1, 0.9 and 0.3, respectively.

Figure 4. Results of experiment E2 with soft evidence SE2 $dir (F_{1}, O_{1}, S)$ and SE3 $dir (O_{2}, F_{1}, SE)$ $dir (O_{2}, O_{1}, SE)$ across scenarios S1–3 ().

Figure 5. Results of experiment E3 with soft evidence SE2, SE4 and SE5 across scenarios S1–3 ().

Figure 6. Examples of possible configuration of objects O₁, O₂, F₁ and F₂ consistent with evidence SE2, SE4 and SE5 in experiment E3 ().

Figure 6. Examples of possible configuration of objects O1, O2, F1 and F2 consistent with evidence SE2, SE4 and SE5 in experiment E3 (Table 6).

Figure 7. Results of experiment E4 with evidence SE2–5 across scenarios S1–3 ().

Figure 8. Examples of possible configuration of points O₁, O₂, F₁ and F₂ consistent with evidence SE3–6 in experiment E4 ().

Figure 8. Examples of possible configuration of points O1, O2, F1 and F2 consistent with evidence SE3–6 in experiment E4 (Table 6).

Figure 9. Results of experiment E5, extending experiment E2 with additional soft evidence for the direction relation between O₁ and F₁ ().

Figure 9. Results of experiment E5, extending experiment E2 with additional soft evidence for the direction relation between O1 and F1 (Table 7).

Figure 10. Three possible scenarios for inconsistent evidence where exactly one piece is neglected for each scenario (faded in graph).

Figure 11. Results of experiment E6, extending experiment E2 with inconsistent evidence for the direction relation between O₁ and O₂, based on scenarios S1–3 in . The figure shows the spatial configuration from the left graph of only as an example (the configuration is strongly counter indicated by the resulting probabilities in scenario S3).

Figure 11. Results of experiment E6, extending experiment E2 with inconsistent evidence for the direction relation between O1 and O2, based on scenarios S1–3 in Table 8. The figure shows the spatial configuration from the left graph of Figure 10 only as an example (the configuration is strongly counter indicated by the resulting probabilities in scenario S3).

Table 4. Truth values for groundings of formula F₁ in the world W_a, W_b and W_c.

Display Table

Table 5. MLN rule base for point-based CDC relation.

Display Table

Table 6. Experimental setup for experiments E1–4 with evidential statements SE1–5 and associated probability scenarios S1–3.

Display Table

Table 7. Experimental setup for experiment E5, extending experiment E2 with additional soft evidence SE2a and SE2b and associated probability scenarios S1–3.

Display Table

Table 8. Experimental setup for experiment E6 with soft evidence SE6–8 and associated probability scenarios S1–3.

Display Table

Data and codes availability statement

The data and codes that support the findings of this study are available through Figshare at the link https://doi.org/10.6084/m9.figshare.21951047.v4.

Qualitative spatial reasoning with uncertain evidence using Markov logic networks

Table A1. MLN rule base for RCC-5.

Table A2. Exhaustive MLN rule base for CDC.

Table A3. MLN rule base for Allen’s interval algebra.

Table 1. Illustration of RCC relations.

Table 2. MLN rule-base for east–west calculus.

Table 3. Truth values for predicates in possible worlds W_a, W_b and W_c.

Table 4. Truth values for groundings of formula F₁ in the world W_a, W_b and W_c.

Table 5. MLN rule base for point-based CDC relation.

Table 6. Experimental setup for experiments E1–4 with evidential statements SE1–5 and associated probability scenarios S1–3.

Table 7. Experimental setup for experiment E5, extending experiment E2 with additional soft evidence SE2a and SE2b and associated probability scenarios S1–3.

Table 8. Experimental setup for experiment E6 with soft evidence SE6–8 and associated probability scenarios S1–3.

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Qualitative spatial reasoning with uncertain evidence using Markov logic networks

Figures & data

Table A1. MLN rule base for RCC-5.

Table A2. Exhaustive MLN rule base for CDC.

Table A3. MLN rule base for Allen’s interval algebra.

Table 1. Illustration of RCC relations.

Table 2. MLN rule-base for east–west calculus.

Table 3. Truth values for predicates in possible worlds Wa, Wb and Wc.

Table 4. Truth values for groundings of formula F1 in the world Wa, Wb and Wc.

Table 5. MLN rule base for point-based CDC relation.

Table 6. Experimental setup for experiments E1–4 with evidential statements SE1–5 and associated probability scenarios S1–3.

Table 7. Experimental setup for experiment E5, extending experiment E2 with additional soft evidence SE2a and SE2b and associated probability scenarios S1–3.

Table 8. Experimental setup for experiment E6 with soft evidence SE6–8 and associated probability scenarios S1–3.

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Table 3. Truth values for predicates in possible worlds W_a, W_b and W_c.

Table 4. Truth values for groundings of formula F₁ in the world W_a, W_b and W_c.