The formal treatment of knowledge and change we develop aims at programming rational agents for practical implemen- tations. Faced with the task of implementing an agent’s men- tal state, two features are most desirable by a reasoner in order to exploit DECKT’s full potential:
• It should enable reasoning to progress incrementally to allow for run-time execution of knowledge-based pro- grams, where an agent can benefit from planning with the knowledge at hand (online reasoning). Each time a program interpreter adds a new action to its agenda, the reasoner should update its current KB appropriately. • It should permit reification of the epistemic fluents in
Event Calculus predicates, to allow for instance the epistemic proposition Knows(Open(S1)) to be han- dled as a term of a first-order logic rather than an atom. Based on this syntactical treatment proposition HoldsAt(Knows(Open(S1)), 0) can be regarded as a well-formed formula.
Most existing Event Calculus reasoners do not satisfy the lat- ter requirement, while only recently an online reasoner was released based on the Cached Event Calculus [Chesani et al., 2009]. Consequently, in order to implement and evaluate dif- ferent use cases we have constructed an Event Calculus rea- soner on top of Jess5, a rule-based engine that deploys the
efficient Rete algorithm for rule matching. Predicates are as- serted as facts in the reasoner’s agenda, specified by the fol- lowing template definition:
(deftemplate EC (slot predicate)
(slot event (default nil)) (slot epistemic (default no))
5
Jess, http://www.jessrules.com/ (last accessed: May 2011)
(multislot posLtrs ) (multislot negLtrs ) (slot time (default 0)))
Multislots create lists denoting fluent disjunctions (conjunc- tions are decomposable into their components according to the definition for knowledge). For instance, knowledge about formula (f1∨ f2∨ ¬f3) at time 1 is captured by the fact: (EC (predicate HoldsAt)
(epistemic Knows) (posLtrs f_1 f_2) (negLtrs f_3) (time 1))
The exploitation of lists for maintaining positive and nega- tive literals of formulae enables the representation of HCDs in a syntax-independent manner, so that all meta-axioms of DECKT be translated into appropriately defined rules. This way, the reasoning process can be fully automated, despite the fact that the (KT6) set is time-dependent: the meta-axioms adapt to the facts that exist in the reasoner’s agenda at each timepoint. Among the basic features of the new reasoner6are: • given a domain axiomatization, the user can select be- tween the execution of classical Event Calculus reason- ing or epistemic reasoning using DECKT.
• the domain axiomatization is written based on a sim- ple, intuitive Event Calculus-like syntax, which is then parsed into appropriate Jess rules (Figure 2). The user may modify the Jess program as well, thus augmenting the axiomatization with advanced and more expressive components, such as rules and constraints not yet sup- ported by the Event Calculus parser.
• new events and observations can be asserted on-the-fly, based on information acquired at execution time, e.g., from the user or the agent’s sensors.
• reasoning can progress incrementally, while the user can decide the time span of the execution step.
• a GUI is provided for modifying and storing Event Cal- culus or Jess programs, for visualizing the output and for providing input to the reasoner at execution time. We should note, though, that the implementation of DECKT described here is general enough to be written in any prolog-like syntax and is not restricted to the Jess tool.
7
Conclusions
The DECKT framework has been used to extended bench- mark commonsense problems with incomplete knowledge, e.g., those included in [Mueller, 2006]. It is also integrated in an Ambient Intelligence project that is currently in progress in our institute, which introduces highly demanding challenges within dynamic environments. The benefits of HCDs are in- vestigated in a number of other interesting aspects in cogni- tive robotics as well, such as for representing the potential effects of physical actions in unknown worlds, on whose oc- currences the agent can only speculate, as well as for tempo- ral indeterminacy of events. Among our future goals is also to extend the applicability of the new reasoner, constituting it a usable educational tool for epistemic action theories.
6
Figure 2: The Jess-EC Reasoner with epistemic capabilities: the Event Calculus domain is translated into Jess rules, whose input and execution the user can modify at execution time.
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