Spatio-Temporal Abduction for Scenario andNarrative Completion

(A Preliminary Statement)

Mehul Bhatt1 and Gregory Flanagan2

Abstract. Hypothetical reasoning is a form of inference that is use-ful in many application domains within the purview of dynamic spa-tial systems. Within a spatial context, this form of inference neces-sitates the ability to model (abductive) explanatory reasoning capa-bilities in the integrated context of formal spatial calculi on the onehand, and high-level logics of action and change on the other.

We present preliminary results by demonstrating the manner inwhich this form of explanatory reasoning may be implementedwithin the framework of the Event Calculus, which is a high-levelformalism for representing and reasoning about actions and their ef-fects. We use an example from the domain of automatic (virtual) cin-ematography / story-visualization and story-boarding, where the ob-jective is to control camera / perspectives and animate a scene on thebasis of apriori known film-heuristics and partial scene descriptionsavailable from discourse material. Underlying the example domainlies the ability to perform spatio-temporal abduction in a generic con-text.

1 Introduction

Hypothetical reasoning about ‘what could be’ or ‘what could havebeen’ on the basis of, and possibly instead of, ‘what is’ is a form ofinference that is useful in many applications involving representingand reasoning about dynamic spatial knowledge. Many applicationinstances within fields such as cognitive robotics, dynamic / event-based GIS, ambient / smart environments, and spatial design may allbe considered to be within the scope of a class of dynamic spatialsystems that require hypothetical reasoning capabilities in specific,and the ability to reason about space, actions and change in an inte-grated manner in general [5]. Both from a representational as well asa computational viewpoint, the basic set of requirements in all theseapplication domains remains the same. Primarily, the following maybe deemed important:

1. Qualitative scene modeling: the capability to abstract from pre-cise geometric modeling of scenes and agent perspectives (e.g.,of robots, avatars) by the use of qualitative spatial representationcalculi pertaining to various aspects of space such as topology,orientation, directions, distance, size

2. Static scenario inference: given partial scene descriptions consist-ing of sets of spatial relationships between domain entities, thederivation of complete scene models by the application of con-

1 SFB/TR 8 Spatial Cognition, University of Bremen, Germany. email:bhatt@informatik.uni-bremen.de

2 Department of Computer Science, CalPoly, USA

straint reasoning algorithms that infer the implicit spatial relation-ships from the explicit ones by exploiting the relational propertiesof the spatial calculi being utilized

3. Scenario and narrative completion: this is the most general case,where given partial narratives that describe the evolution of a sys-tem (e.g., by way of temporally ordered scene observations of arobot, event-based GIS datasets) in terms of high-level positionaland occurrence information, the ability to derive completions thatbridge the narrative by interpolating the missing spatial and action/ event information in a manner that is consistent with domain-specific and domain-independent rules / dynamics

Whereas (1) and (2) involve static scenario inference in a strictlyspatial sense, (3) necessitates commonsense reasoning about space,actions / events and change in an integrated manner [5]. The un-derlying intuition here being that spatial configurations in both realand virtual setups change as a result of interaction (i.e., actions andevents) in the environment and that the formulation of hypothesisabout perceived phenomena is closely connected to the commonsen-sical notions of interaction (e.g., manipulation, movement) in the realworld. For instance, within a GIS, spatial changes could denote (en-vironmental) changes in the geographic sphere at a certain temporalgranularity and could bear a significant relationship to natural eventsand human actions, e.g., changes in land-usage, vegetation, clustervariations among aggregates of demographic features, and wild-lifemigration patterns. Here, event-based and object-level reasoning atthe spatial level could serve as a basis of explanatory analyses, forinstance by abduction, within a GIS [11, 16, 36]. Similarly, within abehavior monitoring and/or security system for a smart environment(e.g., home, office), recognition of dynamic scenes from changesin pre-designated configurations of qualified spatial configurationscould be used as a basis of behaviour monitoring, activity recogni-tion, alert generation and so forth [6, 8, 15].

From a computational viewpoint, hypothetical reasoning withinthe class of aforediscussed dynamic spatial systems requires a formof abductive explanation capability that may be implemented with aformal logic of action and change. This in turn necessitates the em-bedding of qualitative spatial calculi— i.e., the high-level axiomaticconstitution of qualitative calculi —within a particular logic of actionand change that is intended to be utilized [3, 4, 5].

In this paper, we demonstrate the manner in which explanatoryreasoning may be implemented within the framework of the EventCalculus, which is a high-level formalism for representing and rea-soning about actions and their effects. Specifically, we illustrate howspatio-temporal abduction may be directly realized with the discreteversion of the Event Calculus (available as a reasoning engine) in

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(a) SCC andDCC Partitioning

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(b) TheOPRA2 relation ~A 2∠17~B

Figure 1: Orientation Systems

the context of qualitative spatial calculi. We use an example from thedomain of automatic-cinematography / story-visualization and story-boarding, where the objective is to control a camera and / or animatea scene on the basis of apriori known film-heuristics and partial scenedescriptions available from discourse material.

2 Space and Change: Preliminaries

2.1 Qualitative Spatial Reasoning

The field of Qualitative Spatial Reasoning (QSR) investigates ab-straction mechanisms and the technical computational apparatus forrepresenting and reasoning about space within a formal, non-metricalframework [10]. Logical formalizations of space and tools for ef-ficiently reasoning with them are now well-established [29]. For-mal methods in spatial representation, referred to as spatial calculi,may be classified into two groups: topological and positional calculi.When a topological calculus such as the Region Connection Calculus(RCC) [28] is being modeled, the primitive entities are spatially ex-tended and could possibly even be 4D spatio-temporal histories (e.g.,in a domain involving the analyses of motion-patterns). Alternately,within a dynamic domain involving translational motion in a plane,a point-based (e.g., Double Cross Calculus [14], OPRAm [22] )or line-segment based (e.g., Dipole Calculus [30]) abstraction withorientation calculi suffices.

In addition to ontological differences with respect to the nature ofthe primitive spatial entities, i.e., points, line-segments or spatiallyextended bodies, multiple viewpoints also exists with respect to theconceptualization of orientation relations themselves. In general, ori-entation either refers to the direction in which one object is situatedrelative to another, or the direction in which an object is pointing. Thefamily of point-based orientation calculi define the direction of a lo-cated point to a reference point with respect to a perspective point[14]. Within this approach, three axes are used, one is specified bythe perspective point and the reference point, the other two axes areorthogonal to the first one and are specified by the reference pointand the perspective point respectively. These axes define 15 differentternary base relations.

The Single and the Double Cross Calculi [14] use points and or-thogonal lines to partition the space in a finite number of locations,which could take the form of points, lines and extended regions (SeeFig. 1). Similarly, Fig. 1(b) illustrates one primitive relationship forthe Oriented Point Relation Algebra (OPRA) [22], which is a spa-tial calculus consisting of oriented points (i.e., points with a direc-tion parameter) as primitive entities. The granularity parameter mdetermines the number of angular sectors, i.e., the number of baserelations. Applying a granularity of m = 2 results in 4 planar and4 linear regions (Fig. 1(b)), numbered from 0 to 7, where region 0

coincides with the orientation of the point. The family of OPRAm

calculi are designed for reasoning about the relative orientation re-lations between oriented points and are well-suited for dealing withobjects that have an intrinsic front or move in a particular direction.

2.2 The Event Calculus

The Event Calculus is a logical language for reasoning about actionsand change [20, 33]. It defines a set of predicates and axioms thatprovide an inference mechanism to decided “what is true when”. Inthis paper we use a version of the Event Calculus, which is restrictedto the domain of discrete time, referred to as the Discrete Event Cal-culus [23].

The (discrete) Event Calculus defines a fluent as a boolean propertythat represents a value that can change by direct or indirect effects ofan event. Fluents can represent a numerical value of a quality, suchas the temperature of a room, or a boolean proposition, such as itis cold. Additionally, fluents adhere to the commonsense notion ofinertia, which states that a fluents value can only be changed by theeffects of an event. Therefore, if some fluent is true at time-point t0,it will necessarily be true at some later time-point t1, unless an eventoccurs between t0 and t1 such that it effects the value of the fluent.

The Event Calculus provides a set of predicates and axioms to rep-resent problem domains. The HoldsAt predicate defines when a flu-ents holds for a certain value; the Happens predicate defines whenan event happen; and the Initiates, Releases, Terminates predicatesexpress the effects events have on fluents. The following axioms re-late the Discrete Event Calculus predicates to the properties of thecalculus as described above.

HoldsAt(f, t + 1) ⇐ HoldsAt(f, t),∧¬ReleasedAt(f, t + 1)∧

∃e.(Happens(e, t) ∧ Terminates(e, f, t)))(1a)

HoldsAt(f, t + 1) ⇐ Happens(e, t),∧Initiates(e, f, t) (1b)

¬HoldsAt(f, t + 1) ⇐ ¬HoldsAt(f, t),∧¬ReleasedAt(f, t + 1)¬∧

∃e.(Happens(e, t) ∧ Initiates(e, f, t)))(1c)

¬HoldsAt(f, t + 1) ⇐ Happens(f, t),∧Terminates(e, f, t) (1d)

Axioms (1a–1b) ensure the common-sense notion of inertia is en-forced over fluents. (1a) states that a fluent f holds true at a time-point t + 1 if it held true at time-point t and that it was not releasedfrom it’s inertia from the effect of an event. 1a additionally statesthat a fluent is true at a time-point t + 1 if an event occurs at t, whichcauses the fluent to be true. 1c and 1d describe the conditions whena fluents does not hold. A detailed discussion of the Event Calculusformalism is not necessary for this paper, but may be consulted inauthoritative sources [23, 33].

3 The Domain of Automatic Cinematography

Automatic cinematography aims to derive a sequence of camerashots (i.e. the camera’s perspective / orientation to the actors, cam-era’s focus, and angle of view, etc.) from descriptions provided in ascript [18] [9] [12]. In practice, most automatic cinematography in-volves using a knowledge-base of filming heuristics to control theperspective / placement of a camera based on contextual cues of thescene. In this context, a film can be viewed as a hierarchy [18]; thetop of the film hierarchy is the script, which consists of a sequenceof time-ordered narrative descriptions, referred to as scenes. Eachscene, in turn, provides contextual information, in the form of actions

Figure 2: Artistic Impression of a Storyboard.

and events that can be used to derive a specific camera shot. The ob-jective of each camera shot is to capture the sequence of events in amanner that is cinematically pleasing.

As an example, lets look at the simple, but common, scene in Fig.2 depicting a group of two actors in a conversation. A storyboard,such as in Fig. 23, is typically an artist’s impression on the basis ofa film/drama script/screenplay. Within this scenario, the context ofeach scene is based on the current state of each actor with regardsto their participation in the conversation, i.e. talking, listening, orreacting. Below is a sample script that involves two actors, Kendraand Annika, engaged in a conversation. In the example, contextualcues are provided as key words that indicate the current state of eachactor, i.e. “Kendra starts to talk” and “Annika reacts sheepishly” andso forth:

ACT 1: Kendra and Annika[Establishing-shot] -- Kendra and Annika

Kendra starts talking to Annika--[‘‘dialogue’’]

[Cut: mid-shot] -- Annika reacts anxiously to Kendra

Kendra continues talking to Annika

[Cut: Close-up] Annika responds to

Kendra--[‘‘astonish’’]

End.

As the scenes progress the states of each actor change as the con-versation develops. From this information, it is the job of the (au-tomatic) cinematographer to decide on an appropriate sequence ofcamera shots to properly depict the conversation. The result of thisprocess is similar to the storyboard found in Figure 2., which showsthe the perspective of the camera throughout the key moments of thescene. Because this scenario is so common in film, cinematic patternshave emerged that defined heuristics to capture this particular type ofsituation, referred to by cinematographers as a film idiom [2]. Theseidioms have been defined for many typical cinematic situations, suchas groups of actors in a conversation, or an action sequence. In gen-eral, a film idiom can be seen as a set of declarative rules that specifya mapping between the use of camera shots to a situational context.We formally build-up on these aspects in the sections to follow.

3 Source: http://upload.wikimedia.org/wikiversity/en/e/e4/Mok_Thumbnail_storyboards_tiny2.png

4 Explanation by Spatio-Temporal Abduction

Diametrically opposite to projection and planning is the task of post-dictum or explanation [25, 27], where given a set of time-stampedobservations or snap-shots, the objective is to explain which eventsand/or actions may have caused the observed state-of-affairs. Expla-nation, in general, is regarded as a converse operation to temporalprojection essentially involving reasoning from effects to causes, i.e.,reasoning about the past [31].

4.1 Narratives

Explanation problems demand the inclusion of a narrative descrip-tion, which is essentially a distinguished course of actual eventsabout which we may have incomplete information [21, 26]. Narra-tive descriptions are typically available as observations from the real/ imagined execution of a system or process. Since narratives inher-ently pertain to actual observations, i.e., they are temporalized, theobjective is often to assimilate / explain them with respect to an un-derlying process model and an approach to derive explanations.

In the automatic cinematography domain set-out in Section 3, nar-rative descriptions are (implicitly) available from linguistic descrip-tions about acts and scenes within a drama or film script.4 Here, withthe understanding that the progression of the script can be thought ofas an imaginary evolution of the system, the symbolically groundedinformation from the script is equivalent to temporally ordered ob-servations that constitute the available narrative.

266666666664

Φ1 ≡ ¬HoldsAt(Talking(Kendra), t1) ∧ ¬HoldsAt(Talking(Annika), t1)∧

¬HoldsAt(Reacting(Annika), t1) ∧ ¬HoldsAt(Reacting(Kendra), t1)

Φ2 ≡ HoldsAt(Talking(Kendra), t2) ∧ ¬HoldsAt(Talking(Annika), t2)∧

¬HoldsAt(Reacting(Annika), t2) ∧ ¬HoldsAt(Reacting(Kendra), t2)

Φ3 ≡ HoldsAt(Talking(Kendra), t3) ∧ ¬HoldsAt(Talking(Annika), t3)∧

HoldsAt(Reacting(Annika), t3) ∧ ¬HoldsAt(Reacting(Kendra), t3)

377777777775(2a)

[ t1 < t2 < t3] (2b)

(Spatial) Narratives in the Film Domain

One of the key creative roles of a cinematographer / director or astory-boarding artist is to anticipate / visualize the scene on the basisof applicable film-idioms / heuristics (Section 3) that are suited tofilming a particular scenario / narrative, such as the one exemplifiedin (4). For instance, in the context of the ongoing example, the appli-cable idioms are EstablishingShot, ExternalShot and ReactionShot.2664

Φ1 → EstablishingShot(actor1, actor2)

Φ2 → ExternalShot(actor1, actor2)

Φ3 → ReactionShot(actor)

3775 (3)

Each of these film heuristics have a specific structural form that isidentifiable with respect to relative orientation of the camera and the

4 We ignore the translation from a linguistic to a symbolic/predicated form;this is beyond the scope of the objective of this paper.

Camera

Actor 1 Actor 2

(a) Establishing Shot

Camera

Actor 1 Actor 2

(b) External Shot

Camera

Actor 1 Actor 2

(c) Reaction Shot

Figure 3: Structural Form of Film Idioms (Automatic Cinematography: 2 Avatars and 1 Virtual Camera)

actors involved in a scene or the applicable film idiom5:

2664(∀ t). HoldsAt(EstablishingShot(actor1, actor2), t) →

HoldsAt(φscc(camera1, actor1, actor2, scc3), t)∧

HoldsAt(φscc(camera1, actor2, actor1, scc5), t)

3775 (4a)

2664(∀ t). HoldsAt(ExternalShot(actor1, actor2), t) →

HoldsAt(φscc(camera1, actor1, actor2, scc1), t)∧

HoldsAt(φscc(camera1, actor2, actor1, scc5), t)

3775 (4b)

2664(∀ t). HoldsAt(ReactionShot(actor1, actor2), t) →

HoldsAt(φscc(camera1, actor1, actor2, scc4), t)∧

HoldsAt(φscc(camera1, actor2, actor1, scc4), t)

3775 (4c)

Consider the illustration in Fig. 3 for the present film domain: theworld consists of three point-abstracted entities— 2 avatars and 1virtual camera.6 Further, suppose that container space is modeleda discrete grid world together with relative orientation relationshipsamong the entities as per the partitioning scheme of the Single-CrossCalculus (see Section 2.1, Fig. 1). For this ongoing “Kendra and An-nika” script, further suppose that the camera is the only entity thatis able to move, i.e., change location from one grid-cell to another.For a scenario such as this, explanation by spatio-temporal abductioncould serve as a basis of scenario and narrative completion, and forthis particular example, the derivation of ideal camera placements asa side-effect of the abduction process. The general structure of suchas derivation is explained next, and the ongoing example is furthercontinued in Section 4.2.

Structure of (Abductive) Explanation

It is easy to intuitively infer the general structure of narrative com-pletion (by abductive explanation). Consider the illustration in Fig. 4for a branching / hypothetical situation space that characterizes thecomplete evolution of a system. In Fig. 4 – the situation-based his-tory < s0, s1, . . . , sn > represents one path, corresponding to anactual time-line < t0, t1, . . . , tn >, within the overall branching-tree structured situation space. Given incomplete narrative descrip-tions, e.g., corresponding to only some ordered time-points (suchas in Fig. 3) in terms of high-level spatial (e.g., topological, orien-tation) and occurrence information, the objective of explanation isto derive one or more paths from the branching situation space, that

5 This may be easily generalized to n actors/entities in the scene. Further,note that the formal interpretation of the spatial / structural form of an id-iom is open-ended, and subject to the richness of the spatial calculi andother aspects (e.g., scene illumination) being modeled. For the purposes ofthis example, we restrict to an interpretation strictly in terms of orientationrelationships.

6 The third entity in the simulation is a virtual camera that records the othertwo entities in the scene, and hence is not visible within the 3D illustrationof Fig. 3(c).

could best-fit the available narrative information. Of course, the com-pletions that bridge the narrative by interpolating the missing spatialand action/event information have to be consistent with both domain-specific and domain-independent rules/dynamics.

t0

tn

t0

a c

tna

b c

s0 …..

…..

…..s1

si

sn

ti

tj

Figure 4: Branching / Hypothetical Situation Space

Many different formalizations of spatio-temporal explanation arepossible, such as within a belief revision framework [1], nonmono-tonic causal formalizations in the manner of [17], Situation Calculus[3, 4, 32] and so forth; this paper is a pragmatic illustration of themanner in which this may be achieved in the context of the discreteEvent Calculus [20, 24].

4.2 Scenario and Narrative CompletionFigure 5 consists of a narrative (completion), starting with time-points t1 and ending at time-point t12: this denotes an abduced evo-lution of the system, as represented by the sequence of qualitativestate descriptions for 2 stationery and 1 moving entity. For clarity,images from a 3D simulation are included together with the rela-tional / graph-based illustrations for each of the time-points.

The narrative completion is abduced from an initial narra-tive description consisting of observations only of time-points[t1, t4, t6, t8, t12]. Precisely, from the available observations, thenarrative completion has been abduced on the basis of available cam-era actions – pan, zoom, move – and pre-specified knowledge orheuristics / film-idioms about desired camera placements, e.g., estab-lishing shot, external shot, mid-shot, close-up and so forth. Needlessto say, we have excluded one key representational aspect: the descrip-tion so far has only focussed on the domain-specific representationalaspects, and details about encoding the semantics of the spatial cal-culus, in this case the single-cross relations, have been excluded sofar. The spatio-temporal abduction actually works on the basis of theembedding of all the high-level axiomatic aspects of the spatial cal-culus, together with the domain-theory of the “film world’. Withoutthe embedding, spatial calculi— composition theorems, continuityconstraints — have no semantic interpretation within the Event Cal-culus reasoner.

We further discuss the embedding of the spatial calculus withinthe Discrete Event Calculus in Section 4.3. Here, we conclude the

t1

Camera

Actor 1 Actor 2

t2

Camera

Actor 1 Actor 2

t3

Camera

Actor 1 Actor 2

t4

Camera

Actor 1 Actor 2

t5

Camera

Actor 1

Actor 2

t6

Camera

Actor 1 Actor 2

t7

Camera

Actor 1

Actor 2

t8

Camera

Actor 1 Actor 2

t9

Camera

Actor 1

Actor 2

t10

Camera

Actor 1 Actor 2

t11

Camera

Actor 1Actor 2

t12

Camera

Actor 1

Actor 2

Figure 5: Scenario and Narrative Completion (by Abduction).

demonstration of the application with the remark that for this exam-ple, the resulting narrative completion is usable by a virtual realityand/or an automatic cinematography system to automatically gener-ate animations and / or perspective visualizations for automatic story-boarding.

4.3 Embedding Spatial CalculiIn order to derive a spatio-temporal narrative completion directly onthe basis of the semantics of the Discrete Event Calculus (DEC) rea-soner, it is necessary to encode the high-level axiomatic aspects thatdetermine the constitution of a qualitative spatial calculus. For theexample under consideration in this paper, one only needs to en-code certain key aspects of the Single/Double-Cross calculus (in ad-dition to the domain-theory). Precisely, the following aspects needto be modelled explicitly: jointly exhaustive and pair-wise disjoint-ness (JEPD) of the base relations, the composition theorems and thecontinuity constraints of the relationship space.

4.3.1 JEPD Property

Orientational spatial relations, such as those defined by the Single-Cross calculus, are jointly exhaustive, mutually disjoint and pairwisedisjoint. The property of jointly exhaustive and mutually disjoint canbe sufficiently expressed in the DEC using n state constraints of theform (5), where n is the number of total base relations defined by thecalculus. 2666666666666666664

(∀ t).¬[HoldsAt(φscc(o1, o2, o3, scc0), t)∨

HoldsAt(φscc(o1, o2, o3, scc1), t)∨

HoldsAt(φscc(o1, o2, o3, scc2), t)∨

HoldsAt(φscc(o1, o2, o3, scc3), t)∨

HoldsAt(φscc(o1, o2, o3, scc4), t)∨

HoldsAt(φscc(o1, o2, o3, scc5), t)∨

HoldsAt(φscc(o1, o2, o3, scc6), t)] ≡def

HoldsAt(φscc(o1, o2, o3, scc7), t))

3777777777777777775

(5a)

"(∀ t).¬[HoldsAt(φscc(o1, o2, o3, scc0), t)∧

HoldsAt(φscc(o1, o2, o3, scc1), t)])

#(6a)

"(∀ t).¬[HoldsAt(φscc(o1, o2, o3, 1), t)∧

HoldsAt(φscc(o1, o2, o3, 2), t)])

#(6b)

Similarly, the property of pairwise disjointness can be expressedusing [n(n - 1)/2] ordinary constraints of the form in (6).

4.3.2 Composition Theorems

The composition theorems of the Single-Cross calculus have to rep-resented in the DEC using state constraints. For Single-Cross, thisformulation requires 8 X 8 state constraints of the form in (7).

266666664

(∀ t). [HoldsAt(φscc(o1, o2, o3, scc0), t) ∧HoldsAt(φscc(o2, o3, o4, scc0), t)]

→ HoldsAt(φscc(o1, o2, o4, scc4), t)

(∀ t). [HoldsAt(φscc(o1, o2, o3, scc1), t) ∧HoldsAt(φscc(o2, o3, o4, scc1), t)]

→ HoldsAt(φscc(o1, o2, o4, scc5), t) ∨HoldsAt(φscc(o1, o2, o4, scc6), t)

∨ HoldsAt(φscc(o1, o2, o4, scc7), t)

377777775(7a)

Global compositional consistency of scenario descriptions is a keycontributing factor determining the crucial commonsensical notionof the physically realizability [3, 4] (for model elimination) of narra-tive descriptions during the abduction process 7.

4.3.3 Conceptual Neighborhood

The conceptual neighborhood graph [13] for a set of spatial relationsreflects their corresponding continuity structure, namely the the di-rect, continuous transformations that are possible among the relationsas a result of motion by translation and / or deformation. Lets assumethat the binary (reflexive) predicate neighbour(γ1, γ2) denotes thepresence of a continuity relation between qualitative relations γ1 andγ2. 2664

ConceptualNeighbor(scc0, scc1)

ConceptualNeighbor(scc1, scc2)

ConceptualNeighbor(scc6, scc5)

3775 (8)

Given this, one only needs to represent one predicate per continu-ity link of the form in (8) as reflected by a particular partitioning ofthe spatial calculus being utilized, which in this case, is the Single-Cross calculus.

7 Other factors, not relevant for the example of this paper, are physical andexistential consistency [3, 4].

5 Discussion and OutlookThe logic-based integration of specialized spatial representation for-malisms on the one hand and general logics for reasoning about ac-tions and change is an initiative that defines the broad agenda ofthe work described in this paper. The preliminary results presentedherein are guided by the proposition of integrated Reasoning aboutSpace, Actions and Change (RSAC) [5], which we regard to be a use-ful paradigm for applications of formal methods in Qualitative Spa-tial Representation and Reasoning (QSR) within realistic DynamicSpatial Systems.

The specific aim of this paper has been to demonstrate the mannerin which spatio-temporal abduction may be performed with an off-the-shelf logic of action and change, namely the Event Calculus, thatis available a reasoning tool. We demonstrate this in the context ofan example “automatic cinematography” domain, which we regardto be intuitively appealing in order to communicate the often con-trived idea of logical explanation by abduction. We emphasize thatautomatic cinematography is not merely a toy domain: in the enter-tainment industry, a wide-range of applications require the to abilityto visualize complex— single agent and multi-perspective —scenesin a dynamic and real-time context. Major applications include auto-matic (virtual) cinematography or in general automatic story visual-ization and story-boarding (as addressed here), real-time perspectivemodeling for games, the modeling of interaction in hybrid or real–virtual environments, e.g., for e-learning, and so forth. As anotheremerging application, consider the domain of spatial computing fordesign [7]. Here, abductive reasoning in general plays a significantrole in reasoning about hypothetical spatial structures.

From a theoretical perspective, we are presently pursuing the inte-gration of specialized (infinite domain) spatial reasoning tools suchas SparQ [34]and GQR [35] within the Discrete Event Calculus rea-soner; the approach being adopted here is to ensure a separation ofconcerns during the satisfiability checking process (based on the rel-sat solver8) underlying the DEC reasoner. Experiments are also inprogress to achieve a similar sort of integration of spatial reason-ers with not only the relsat solver, but also other extensions intothe answer-set programming (ASP) framework9 [19]. The challengehere lies in maintaining the separation during the constraint solvingstage between the native relsat / ASP solvers that underly the EventCalculus reasoner and specialized spatial reasoning tools, i.e., theobjective here is not to replace SAT or ASP solvers, but rather tocomplement their constraint solving capabilities with the aforestatedspecialized spatial reasoning tools. From an application perspective,we are pursuing the application of the proposed spatio-temporal ab-duction mechanism in other application areas of interest, e.g., designcreativity, dynamic GIS, smart environments.

AcknowledgmentsWe gratefully acknowledge the funding and support by the Alexandervon Humboldt Stiftung (Germany) and the German Research Foun-dation (DFG). Gregory Flanagan was supported by a Research Schol-arship (May 2009) by the SFB/TR 8 Spatial Cognition Center.

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theory change: Partial meet contraction and revision functions’, J. Symb. Log.,50(2), 510–530, (1985).

[2] Daniel Arijon, Grammar of the Film Language, Hastings House, New York,1976.

[3] Mehul Bhatt, ‘Commonsense inference in dynamic spatial systems: Phenome-nal and reasoning requirements’, in 23rd International Workshop on QualitativeReasoning (QR 09), Ljubljana, Slovenia, June 2009, eds., Ivan Bratko and JureZabkar, pp. 1–6, (2009). (Part 1 of 2).

[4] Mehul Bhatt, ‘Commonsense inference in dynamic spatial systems: Epistemo-logical requirements’, in FLAIRS Conference: Special Track on Spatial andTemporal Reasoning. AAAI Press, (2010). (Part 2 of 2): to appear.

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