Advances in Knowledge Representation, Logic Programming, and by Thomas Eiter, Hannes Strass, Miroslaw Truszczyński, Stefan

By Thomas Eiter, Hannes Strass, Miroslaw Truszczyński, Stefan Woltran

This Festschrift is released in honor of Gerhard Brewka at the social gathering of his sixtieth birthday and includes articles from fields reflecting the breadth of Gerd's paintings. The 24 medical papers integrated within the publication are written by way of shut neighbors and associates and canopy subject matters reminiscent of activities and brokers, Nonmonotonic and Human Reasoning, personal tastes and Argumentation.

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Put in words, – states are sets of ground fluents; – the initial state is given by all derivable instances of init(f ); – to determine if an action is legal in a state s , this state s has to be encoded using facts true(f ), and then a is possible if legal(a) can be derived; – likewise, to determine the effects of an action a in a state s, the action and the state have to be encoded using facts does(a) and true(f ), respectively, and then the resulting state is given by all derivable instances of next(f ).

For capturing the stable models of such logic programs with externals, we need the following definitions. A (partial) assignment i over a set A ⊆ A of atoms is a function: i : A → {t, f, u}, where A is the set of given atoms. With this, we define At = {a ∈ A | i(a) = t}, Af = {a ∈ A | i(a) = f }, and Au = {a ∈ A | i(a) = u}. In what follows, we represent partial assignments either by At , Af or At , Au by leaving the respective default value implicit. 4 That is, input atoms are externals that are not overridden by rules in P .

H o r i z o n , n o t p o s ( R , X , Y, T ) . 29 :− move ( R , DX, DY, T−1) , t i m e ( T ) , n o t goon ( T−1) , n o t move ( R , DX, DY, T ) . 31 # m i n i m i z e{ 1 ,T : goon ( T ) } . The rule in Line 27 indicates whether some goal condition is (not) established at a time point. Once the goal is established, the additional integrity constraint in Line 29 ensures that it remains satisfied by enforcing that the goal-achieving move is repeated at later steps (without altering robots’ positions).

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