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 celebration of his sixtieth birthday and includes articles from fields reflecting the breadth of Gerd's paintings. The 24 clinical papers integrated within the ebook are written by means of shut pals and associates and canopy themes comparable to activities and brokers, Nonmonotonic and Human Reasoning, personal tastes and Argumentation.

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Next ( cell (X ,Y , Z )) : - does ( move (U ,V ,X , Y )) , true ( cell (U ,V , Z )). = X. Y. X. Y. 31 32 next ( step ( Y )) : - true ( step ( X )) , succ (X , Y ). 33 34 succ (1 ,2). succ (2 ,3). succ (79 ,80). Fig. 2. The 15-puzzle described by an action theory • cell (u, v) becomes empty while the tile is now in (x, y) (clauses 24, 25); • all other cells retain their tiles (clauses 27–30); • the step counter is incremented (clause 25). As can be seen from this example, our action theory uses the following unary predicates as pre-defined keywords: – – – – – init(f ), to define fluent f to be true initially; true(f ), denoting the condition that f is true in a state; does(a), denoting the condition that a is performed in a state; legal(a), meaning that action a is possible; next(f ), to define the fluents that are true after an action is performed.

Thielscher irrelevant for the question whether a game is playable and because our action language of Definition 1 is in fact a stripped-down version of GDL, the formal concept of simulation of action theories, along with our proof technique, can be employed for the purpose of automatically proving that a game is playable in a robotic environment. The only requirement is to symbolically describe the latter by an action theory in the same language. 6 Conclusion In this paper we have defined the concept of one action theory being able to simulate a second one.

Coord (a ,1). coord (a ,2). coord (a ,3). coord (x ,1). coord (x ,2). coord (x ,3). coord (a ,4). coord (x ,4). Fig. 3. An action theory describing the physical environment of the robot in Fig. 1 Example. The action theory in Fig. 3 describes the physical environment of the robot in Fig. 1 with the help of a single fluent, piece(i, j), indicating whether a can has been placed at (i, j) where i ∈ {a, b, c, x} and j ∈ {1, 2, 3}; and the action put(i, j, k, l) of lifting the object at location (i, j) and putting it down at location (k, l).

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