ABSTRACT
In the cognitive sciences, image schemas are considered to be the conceptual building blocks learned from sensorimotor processes in early infancy. They are used in language and higher levels of cognition as information skeletons. Despite the potential of integrating image schemas into formal systems to aid for instance common-sense reasoning, computational analogy and concept invention, normalisations of image schemas are sparse. In particular in respect to their dynamic nature. In this paper, we therefore describe how some of the dynamic aspects of the image schema Containment can be formally approached using an image schema logic based on the Region Connection Calculus (RCC8), the Qualitative Trajectory Calculus (QTC), Ligozat's cardinal directions (CD), and Linear Temporal Logic over the reals (RTL), with 3D Euclidean space assumed for the spatial domain. The distinctions in our formalisations are motivated with concrete examples from natural language, derived from semi-automated image schema extraction, and illustrate that we target some of the essential distinctions regarding containers and movement.
- Brandon Bennett and Claudia Cialone. 2014. Corpus Guided Sense Cluster Analysis: a methodology for ontology development (with examples from the spatial domain). In Eight International Conference on Formal Ontology in Information Systems (FOIS) (Frontiers in Artificial Intelligence and Applications), Pawel Garbacz and Oliver Kutz (Eds.), Vol. 267. IOS Press, 213--226.Google Scholar
- Tarek R. Besold, Maria M. Hedblom, and Oliver Kutz. 2017. A narrative in three acts: Using combinations of image schemas to model events. Biologically Inspired Cognitive Architectures 19 (2017), 10--20.Google ScholarCross Ref
- Peter Bogaert, Ruben Maddens Emile van der Zee, Nico Van de Weghe, and Philippe De Maeyer. 2008. Cognitive and linguistic adequacy of the qualitative trajectory calculus. In Proceedings of the International Workshop "From Natural to Formal Language" (In collaboration with "GIScience"). 1--7.Google Scholar
- Roberto Casati and Achille C. Varzi. 1997. Spatial Entities. In Spatial and Temporal Reasoning, Oliviero Stock (Ed.). Springer Netherlands, Dordrecht, 73--96.Google Scholar
- Anthony G. Cohn, Brandon Bennett, John Gooday, and Nick Gotts. 1997. RCC: a calculus for Region based Qualitative Spatial Reasoning. GeoInformatica 1 (1997), 275--316.Google ScholarDigital Library
- Ernest Davis, Gary Marcus, and Noah Frazier-Logue. 2017. Commonsense reasoning about containers using radically incomplete information. Artificial Intelligence 248 (2017), 46--84.Google ScholarCross Ref
- Ellen Dodge and George Lakoff. 2005. Image schemas: From linguistic analysis to neural grounding. In From perception to meaning: Image schemas in cognitive linguistics, Beate Hampe and Joseph E. Grady (Eds.). Mouton de Gruyter, Berlin, 57--91.Google Scholar
- Marcello Finger and Dov M. Gabbay. 1993. Adding a Temporal Dimension to a Logic System. Journal of Logic, Language and Information 1 (1993), 203--233.Google ScholarCross Ref
- Andrew U. Frank and Martin Raubal. 1999. Formal specification of image schemata - a step towards interoperability in geographic information systems. Spatial Cognition and Computation 1, 1 (1999), 67--101. Google ScholarDigital Library
- Antony Galton. 2010. The Formalities of Affordance. In Proc. of workshop Spatio-Temporal Dynamics, Mehul Bhatt, Hans Guesgen, and Shyamanta Hazarika (Eds.). 1--6.Google Scholar
- James J. Gibson. 1977. The theory of affordances, in Perceiving, Acting, and Knowing. Towards an Ecological Psychology. In Perceiving, Acting, and Knowing: Toward an Ecological Psychology, Robert Shaw and John Bransford (Eds.). NJ: Lawrence Erlbaum, Hillsdale, 67--82.Google Scholar
- Dagmar Gromann and Maria M. Hedblom. 2016. Breaking Down Finance: A method for concept simplification by identifying movement structures from the image schema PATH-following. In Proc. of the Joint Ontology Workshops (JOWO).Google Scholar
- Dagmar Gromann and Maria M. Hedblom. 2017. Kinesthetic Mind Reader: A Method to Identify Image Schemas in Natural Language. In Proc. of Advancements in Cognitive Systems.Google Scholar
- Frank Guerin. 2011. Learning like a baby: a survey of artificial intelligence approaches. The Knowledge Engineering Review 26, 2 (2011), 209--236. Google ScholarDigital Library
- Marion Haemmerli and Achille C. Varzi. 2014. Adding Convexity to Mereotopology. In Formal Ontology in Information Systems. Proceedings of the Eighth International Conference, Pawel Garbacz and Oliver Kutz (Eds.). IOS Press, 65--78.Google Scholar
- Torsten Hahmann and Boyan Brodaric. 2013. Kinds of Full Physical Containment. Springer International Publishing, Cham, 397--417. Google ScholarDigital Library
- Maria M. Hedblom, Oliver Kutz, Till Mossakowski, and Fabian Neuhaus. 2017. Between Contact and Support: Introducing a logic for image schemas and directed movement. In Proceedings of the 16th International Conference of the Italian Association for Artificial Intelligence (AI*IA 2017) (LNAI). Springer, Bari, Italy, 256--268. Accepted for publication, forthcoming.Google ScholarCross Ref
- Maria M. Hedblom, Oliver Kutz, and Fabian Neuhaus. 2015. Choosing the right path: image schema theory as a foundation for concept invention. Journal of Artificial General Intelligence 6, 1 (2015), 22--54.Google ScholarCross Ref
- Maria M. Hedblom, Oliver Kutz, and Fabian Neuhaus. 2016. Image schemas in computational conceptual blending. Cognitive Systems Research 39 (2016), 42--57. Google ScholarDigital Library
- Mark Johnson. 1987. The body in the mind: the bodily basis of meaning, imagination, and reason. The University of Chicago Press.Google Scholar
- C. Maria Keet and Oliver Kutz. 2017. Orchestrating a Network of Mereo(topo)logical Theories. In Proceedings of the the 9th International Conference on Knowledge Capture (K-CAP 2017), December 4th-6th, 2017, Austin, Texas, United States. ACM. Google ScholarDigital Library
- Markus Knauff, Reinhold Rauh, and Jochen Renz. 1997. A cognitive assessment of topological spatial relations: Results from an empirical investigation. In Spatial Information Theory: A Theoretical Basis for GIS, Stephen C. Hirtle and Andrew U. Frank (Eds.). LNCS, Vol. 1329. Springer, 193--206. Google ScholarDigital Library
- Roman Kontchakov, Agi Kurucz, Frank Wolter, and Michael Zakharyaschev. 2007. Spatial Logic + Temporal Logic = ? Springer Netherlands, Dordrecht, 497--564.Google Scholar
- Fred Kröger and Stephan Merz. 2008. Temporal Logic and State Systems (Texts in Theoretical Computer Science. An EATCS Series) (1 ed.). Springer Publishing Company, Incorporated. Google ScholarDigital Library
- Werner Kuhn. 2007. An Image-Schematic Account of Spatial Categories. In Spatial Information Theory, Stephan Winter, Matt Duckham, Lars Kulik, and Ben Kuipers (Eds.). LNCS, Vol. 4736. Springer, 152--168. Google ScholarDigital Library
- Werner Kuhn. 2007. An image-schematic account of spatial categories. In Spatial information theory, Stephan Winter, Matt Duckham, Lars Kulik, and Ben Kuipers (Eds.). Springer Berlin Heidelberg, 152--168. Google ScholarDigital Library
- Yohei Kurata and Max Egenhofer. 2007. The 9+-Intersection for Topological Relations between a Directed Line Segment and a Region. In 1st Workshop on Behaviour Monitoring and Interpretation, KI 2007, B. Gottfried (Ed.). 62--76.Google Scholar
- George Lakoff. 1987. Women, fire, and dangerous things. what categories reveal about the mind. The University of Chicago Press.Google Scholar
- Jean M. Mandler. 2004. The Foundations of Mind: Origins of Conceptual Thought: Origins of Conceptual Though. Oxford University Press, New York.Google Scholar
- Jean M. Mandler and Cristóbal Pagán Cánovas. 2014. On defining image schemas. Language and Cognition (2014), 1--23.Google Scholar
- Leora Morgenstern. 2001. Mid-Sized Axiomatizations of Commonsense Problems: A Case Study in Egg Cracking. Studia Logica 67 (2001), 333--384.Google ScholarCross Ref
- Till Mossakowski, Christian Maeder, and Klaus Lüttich. 2007. The heterogeneous tool set, HETS. Tools and Algorithms for the Construction and Analysis of Systems (2007), 519--522. Google ScholarDigital Library
- Todd Oakley. 2010. Image Schema. In The Oxford Handbook of Cognitive Linguistics, Dirk Geeraerts and Hubert Cuyckens (Eds.). Oxford University Press, 214--235.Google Scholar
- David A. Randell, Zhan Cui, and Anthony G. Cohn. 1992. A Spatial Logic based on Regions and Connection. In Proc. 3rd Int. Conf. on knowledge representation and reasoning. Google ScholarDigital Library
- Mark Reynolds. 2010. The complexity of temporal logic over the reals. Annals of Pure and Applied Logic 161, 8 (2010), 1063 -- 1096.Google ScholarCross Ref
- Francisco Santibáñez. 2002. The object image-schema and other dependent schemas. Atlantis 24, 2 (2002), 183--201.Google Scholar
- Martin Schmidt, Ulf Krumnack, Helmar Gust, and Kai-Uwe Kühnberger. 2014. Heuristic-Driven Theory Projection: An Overview. In Computational Approaches to Analogical Reasoning: Current Trends, H. Prade and G. Richard (Eds.). Computational Intelligence, Vol. 548. Springer-Verlag.Google Scholar
- Lawrence Shapiro. 2011. Embodied cognition. Routledge, London and New York.Google Scholar
- Robert St. Amant, Clayton T. Morrison, Yu-Han Chang, Paul R. Cohen, and Carole Beal. 2006. An image schema language. In Proc. of the 7th Int. Conf. on Cognitive Modeling (ICCM). 292--297.Google Scholar
- Mark Steedman Steedman. 2002. Formalizing Affordance. In Proc. of the 24th Annual Meeting of the Cognitive Science Society. 834--839.Google Scholar
- Lisa Walton and Michael Worboys. 2009. An Algebraic Approach to Image Schemas for Geographic Space. In Spatial Information Theory (Lecture Notes in Computer Science), Vol. 5756. Springer, 357--370. Google ScholarDigital Library
- Nico Van De Weghe, Anthony G. Cohn, Guy De Tré, and Philippe De Maeyer. 2006. A qualitative trajectory calculus as a basis for representing moving objects in geographical information systems. Control and cybernetics 35, 1 (2006), 97--119.Google Scholar
- F. Wolter and M. Zakharyaschev. 2000. Spatial reasoning in RCC-8 with Boolean region terms. In Proceedings of the fourteenth European Conference on Artificial Intelligence, ECAI 2000, Berlin, Germany, W. Horn (Ed.). IOS Press, 244--248. Google ScholarDigital Library
Index Terms
- In, out and through: formalising some dynamic aspects of the image schema containment
Recommendations
Computing Circumscription Revisited: A Reduction Algorithm
In recent years, a great deal of attention has been devoted to logics of common-sense reasoning. Among the candidates proposed, circumscription has been perceived as an elegant mathematical technique for modeling nonmonotonic reasoning, but difficult to ...
Many-Valued Modal Non-Monotonic Reasoning: Sequential Stable Sets and Logics with Linear Truth Spaces
A family of many-valued modal logics which correspond to possible-worlds models with many-valued accessibility relations, has been recently proposed by M. Fitting [7, 8]. Non-monotonic extensions of these logics are introduced with a fixpoint ...
Elimination of quantifiers and undecidability in spatial logics for concurrency
Concurrency theory (CONCUR 2004)The introduction of spatial logics in concurrency is motivated by a shift of focus from concurrent systems towards distributed systems. Aiming at a deeper understanding of the essence of dynamic spatial logics, we study a minimal spatial logic without ...
Comments