By Raymond Reiter
Modeling and imposing dynamical structures is a critical challenge in synthetic intelligence, robotics, software program brokers, simulation, choice and regulate thought, and lots of different disciplines. in recent times, a brand new method of representing such platforms, grounded in mathematical common sense, has been constructed in the AI knowledge-representation group. This publication offers a finished remedy of those rules, basing its theoretical and implementation foundations at the state of affairs calculus, a dialect of first-order good judgment. inside of this framework, it develops many beneficial properties of dynamical platforms modeling, together with time, approaches, concurrency, exogenous occasions, reactivity, sensing and information, probabilistic uncertainty, and determination idea. It additionally describes and implements a brand new relatives of high-level programming languages appropriate for writing keep watch over courses for dynamical platforms. eventually, it contains scenario calculus standards for a variety of examples drawn from cognitive robotics, making plans, simulation, databases, and choice conception, including all of the implementation code for those examples. This code is accessible at the book’s website.
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Extra info for Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems
Example text
This is logically equivalent to: F(x, s) ∧ ¬ε− F (x, y, s) ⊃ F(x, do(A(y), s)). A symmetric argument yields the axiom: ¬F(x, s) ∧ ¬ε+ F (x, y, s) ⊃ ¬F(x, do(A(y), s)). These have precisely the syntactic forms of positive and negative frame axioms. Under the Causal Completeness Assumption, there is a systematic way to obtain these frame axioms from the effect axioms. 2: Recall the earlier example effect axiom: f ragile(x, s) ⊃ br oken(x, do(dr op(r, x), s)). 1): x = y ∧ f ragile(x, s) ⊃ br oken(x, do(dr op(r, y), s)).
Such axioms describe deterministic actions, and preclude indeterminate actions with uncertain effects, for example: heads(do( f li p, s)) ∨ tails(do( f li p, s)), (∃x)holding(x, do( pickup Ablock, s)). Effect axioms, and therefore the solution to the frame problem, are for primitive actions only; as yet, there are no constructs for complex actions, like the following: • Conditional actions: if car I n Driveway then drive else walk endif. • Iterative actions: while [(∃ block)ontable(block)] do r emove Ablock endwhile.
N , . }. Notice what this set claims: that (A, B) is in the transitive closure of G, but no finite sequence of edges in the graph G leads from A to B. So this set is obviously unsatisfiable. Now, use the compactness theorem to obtain a contradiction. The above proof assumed that the underlying first-order language had at least two constant symbols A and B. But this assumption is unimportant; it is easy to see that if τ (x, y) defines the transitive closure of G in a first order language, it continues to do so for the enlarged language obtained by adding two new constant symbols A and B to the original language.