Integrating Action Calculi and Description Logics

Abstract

General action languages, like e.g. the Situation Calculus, use full classical logic to represent knowledge of actions and their effects in dynamic domains. Description Logics, on the other hand, have been developed to represent static knowledge with the help of decidable subsets of first-order logic. In this paper, we show how to use Description Logic as the basis for a decidable yet still expressive action formalism. To this end, we use ABoxes as decidable state descriptions in the basic Fluent Calculus. As a second contribution, we thus obtain an independent semantics-based on a general action formalism-for a recent method for ABox-Update.

Verifying UML/OCL Operation Contracts

“…Recent results [11] have extended the description logics formalism (in short, a decidable subset of first-order logic) to define and reason on operation contracts.…”

A description logic based situation calculus

“…Similar to our paper [37], Drescher and Thielscher [21] explored reasoning about actions based on a description logic, but they concentrate on the f luent calculus [85] instead of the situation calculus. Instead of dealing with actions and the changes caused by actions, some of the approaches turned to extensions of description logics with temporal logics to capture the changes of the world over time [1,5], and some others combined planning techniques with description logics to reason about tasks, plans and goals and exploit descriptions of actions, plans, and goals during plan generation, plan recognition, or plan evaluation [32].…”

“…Now we estimate the size of W when R is a fluent according to the way it is constructed above. First, for any n ≥ 0 and any situation S where sitLength(S) = n, we estimate an upper bound on the size of the DNF formula (denoted as g(n) below), which is equivalent to R[R(x, y, S)] and constructed specifically according to the above steps (17)(18)(19)(20)(21). Note that for each i = 1..m + , j = 1..m − and l = 1..n, size(ν + i,l (x)), (size(η + i,l (y)), size(ν − j,l (x)) size(η − j,l (y)), respectively) is no more than h + 2 according to the above for the cases (1)- (16) and (1')-(16') in Table 12.…”

The ramification problem in temporal databases: a solution implemented in SQL

“…At this step we integrate all these causal relationships into one. For example if f 1 ∧ f 2 causes f 3 if f 4 and f 5 ∧ f 6 causes f 3 if f 7 , then the static rule F alse → f 3 is transformed first in f 1 ∧ f 2 ∧ f 4 → f 3 and finally in (…”

“…For example if we evaluate the G s = f 1 ([[3,8]]) ∧ f 2 ([[3,4]])) → f 5 at time point 3, then the fluent f 5 is true at the time interval[3,4] because t min = min{4, 8}. Notice that we estimate a different t min for each static rule.…”