Logic, Ontology and Planning: The Robot’s Knowledge Lectures 3-4 From Conceptual Blending to Computational Concept Invention Stefano Borgo & Oliver Kutz ESSLLI 2018, Sofia, Bulgaria Laboratory for Applied Ontology (LOA), ISTC-CNR, Trento (IT) CORE Conceptual and Cognitive Modelling Group KRDB Research Centre for Knowledge and Data Free University of Bozen-Bolzano, Italy . KRDB 3 Today's topic: Invention • Artificial agents that act autonomously in a changing environment need to - adapt to constant change - find workable solutions to unexpected scenarios • Fully autonomous robots require elements of human creativity to be successful • Key elements are: - Concept invention: combine previously learned/acquired ideas into novel ideas - Use invention to re-purpose available tools for new tasks Concept Invention: A highly interdisciplinary endeavour ... • From Conceptual Blending - Cognitive Linguistics / Embodied Cognition - Metaphor Theory / Analogies - Image Schema Theory • to Computational Concept Invention - Computational Creativity (CC) - Knowledge Engineering / Ontologies - Category Theory / Non-Classical Logic / Computational Logic Concept Invention: A highly interdisciplinary endeavour • Part 1: - what is conceptual blending? • Part 2: - an abstract framework and representation language • Part 3: - cognitive modelling and computational problems ‣ computing generic spaces via generalisation ‣ image schemas as generic spaces Part 1: Conceptual Blending Conceptual Blending ... • Mark Turner (2014): a hypothetical explanation for the ‘human spark’: • The ‘lionman’, approximately 32.000 years old, blends the concepts of ‘human’ and ‘lion’. • The period of its creation marks the end of an apparent deadlock of human cultural development, ... • and the beginning of rapid cultural evolution (hypothesis: expansion of working memory). Conceptual Blending • developed in the early 1990s by Gilles Fauconnier and Mark Turner • intended to understand and model the process of concept invention • much studied within cognitive psychology and linguistics • Conceptual Blending concerns blending of two thematically rather different conceptual spaces yielding a new conceptual space with - emergent structure, selectively combining parts of the given spaces - whilst respecting common structural properties. Summarised by Fauconnier & Turner (2003): • inputs have different organising frames • blend has an organising frame that receives projections • blend has emergent structure on its own • inputs offer the possibility of rich clashes • blends offer challenges to the imagination • resulting blends can turn out to be highly imaginative A foldable toothbrush is not an analogy! Conceptual Blending: Example Note: The diagram is upside-down (motivated by the formal model) Conceptual Blending: Example Conceptual Blending: Houseboat Conceptual Blending: Boathouse Blending Signs and Forests: Input 1 • Signs: a piece of paper, wood or metal that has writing or a picture on it that gives you information, instructions, a warning (Oxford Advanced Learner’s Dictionary) Blending Signs and Forests: Input 2 • Forests complex eco- logical systems in which trees are the dominant life form (Encyclopaedia Britannica) Blending Signs and Forests: Blend 1 Signs in Forests Blending Signs and Forests: Blend 2 Forestsigns Blending Signs and Forests: Blend 3 Signforests "Optimality Principles" (Heuristics): What makes a good blend? • Integration: The blend must constitute a tightly integrated scene that can be manipulated as a unit. • Pattern Completion: complete elements in the blend . • Maximization of Vital Relations: change, identity, time, space, cause-effect, part-whole, . • Unpacking: The blend alone must enable the perceiver to unpack the blend to reconstruct the inputs, the cross- space mapping, the generic space, and the network of connections between all these spaces • Relevance: ... Graphical Representation of a Formal DOL Specification Part 2: Abstract Framework and Representation Language Blending: Formal Model (C + BK) consistent with B (B + BK) entail R Evaluation consistency consequence C R requirements requirements • Creating blends in Ontohub / DOL B • usage of background Input theory 1 I1 Blendoid I2 Input theory 2 ontologies image schemas as I1* I2* • base ontologies Generalised input theory 1 Generalised input theory 2 • evaluation features Base Ontology - constraints - requirements BK Rich Background Knowledge Blending with DOL, Hets, Ontohub • Formal (meta)-language: DOL - describes structured ontologies / models / specifications - supports specification of blending diagrams - specifies requirements for evaluation • Heterogenous reasoning: Hets - proof support for structured ontologies/theories - computation of colimits • Repository for heterogeneous theories: Ontohub - supports a variety of logical languages for ontology, mathematics, music - supports ontology evaluation techniques T. Mossakowski et al. / Three Semantics for DOL 3 DOL intends to cover all state-of-the-art basic ontology languages, and to provide a meta level on top of these. This meta level allows for the representation of logically heterogeneous ontologies in the sense that DOL ontologies may comprise of modules written in ontology languages with different underlying logics. Moreover, the DOL meta level constructs allow for links between ontologies such as relative interpretations or conservative extensions. DOL intends to be an extensible framework for ontology languages. It is intended that any ontology language and any logic whose conformance with DOL has been es- tablished can be used with DOL. In particular, we are interested in establishing the con- formance of a number of widely used ontology languages and logics as a part of the standard; these include (ordered by increasing complexity) propositional logic (Prop), OWL [1] (with its profiles EL, RL and QL [23]), standard first-order logic with equality (FOL DOL=) and Common Logic (CL) [5]5, as well as translations between these ontology languages. Such translations have been developed in previous research; see e.g. [21]. Note in particular that, among these ontology languages, Common Logic is the most expressive- one,relate and (on is therefore the meta-level) a target language ontologies for translations that are from written all the in other lan- guages. Thus,diff whenerent reasoning formalisms. about heterogeneous distributed ontologies, one can prima facie translate all participating ontologies to Common Logic. However, note the differ- • E.g. prove that some OWL version of the ence to translating all ontologies to Common Logic in the first place: when, e.g., an OWL foundational ontology DOLCE is logically entailed ontology has been translated to Common Logic, it is no longer easily amenable to de- cidable or even tractableby the reasoning (reference) procedures first-order that OWL version;tools support. Therefore, DOL leaves all- ontologiesre-use ontology in their original modules formalisation even if they to take have advantage been of the optimised automated reasonersformulated for thatin a particular different language, formalism; and DOL tools should only translate them on demand. In summary,- re-use the ontology functionality tools of the likeDOL theoremframework provers can be capturedand module by the follow- ing “equation”:extractors4 along translations between formalisms. EdNote:4 DOL = meta(Prop,EL,QL,RL,OWL,FOL=,CL,... Prop OWL,Prop FOL,EL OWL,OWL FOL,FOL CL,...) ! ! ! ! ! where the meta( ) operation introduces the above mentioned meta-level constructs on · top of the basic ontology languages using the built-in logic translations. 3. An Introductory Example We use an example from mereology, which lends itself well to heterogeneous formal- isation. While mereological relations such as parthood are frequently used in ontolo- gies, many of these ontologies are formalised in languages that are not fully capable of defining the mereological notions. For example, mereological relations are used in large biomedical ontologies, which are implemented in the EL profile of OWL for efficiency. OWL is partly capable of defining these relations, whereas more complete definitions require first-order or even second-order logic [14]. 5Listing 1 starts with a Prop formalisation of the taxonomy of the categories over EdNote:5 5In the future, we might add other logics such as IKL [10]. 4EDNOTE: CL: TODO review “equation more confusing than useful” 5EDNOTE: @Oliver and then Till: describe informally what the “overall ontology” in this example means Logic Graph supported by DOL bRDF OBOOWL RDF EL++ DL-Lite DL-RL subinstitution UML-CD R Prop (OWL 2 EL) (OWL 2 QL) (OWL 2 RL) theoroidal subinstitution Schema.org SROIQ RDFS simultaneously exact and (OWL 2 DL) model-expansive comorphisms OBO 1.4 model-expansive comorphisms DDLOWL OWL-Full DFOL FOL= ECoOWL grey: no fixed expressivity green: decidable ontology languages F-logic ECoFOL CL- yellow: semi-decidable CL EER orange: some second-order constructs red: full second-order logic ms= FOL CASL HOL DOL: Core Syntax Constructs An ontology O can be, among other cases not covered here, one of the following: - a basic ontology ⟨Σ,∆⟩ written in some ontology language. For simplicity, we assume that it is directly given by a signature Σ and a set of axioms ∆ - a translation “O with logic ρ” of an ontology O along an ontology language translation ρ; - an extension O then CS? ⟨Σ, ∆⟩ of an ontology O by another basic ontology ⟨Σ,∆⟩; the extension can be marked as a conservative extension (CS; model-conservative