Abstract

We consider a modified version of the situation calculus built using a two-variable fragment of the first-order logic extended with counting quantifiers. We mention several additional groups of axioms that can be introduced to capture taxonomic reasoning. We show that the regression operator in this framework can be defined similarly to regression in Reiter’s version of the situation calculus. Using this new regression operator, we show that the projection and executability problems (the important reasoning tasks in the situation calculus) are decidable in the modified version even if an initial knowledge base is incomplete. We also discuss the complexity of solving the projection problem in this modified language in general. Furthermore, we define description logic based sub-languages of our modified situation calculus. They are based on the description logics ALCO(U) (or ALCQO(U), respectively). We show that in these sub-languages solving the projection problem has better computational complexity than in the general modified situation calculus. We mention possible applications to formalization of Semantic Web services and some connections with reasoning about actions based on description logics.

Highlights

  • The situation calculus (SC) is a well known and popular logical theory for reasoning about changes caused by events and actions

  • In this paper we would like to consider the SC from [70] that extends the original SC with time, concurrency, stochastic actions, etc. It serves as a foundation for the Process Specification Language (PSL) that axiomatizes a set of primitives adequate for describing the fundamental concepts of manufacturing processes (PSL has been accepted as an international standard) [31, 30]

  • The major consequence of the results proved above for the problem of service composition is the following

Read more

Summary

Introduction

The situation calculus (SC) is a well known and popular logical theory for reasoning about changes caused by events and actions. Because the situation calculus is formulated in a general predicate logic, reasoning about effects of sequences of actions is undecidable (unless some restrictions are imposed on the theory that axiomatizes the initial state of the world). We consider a fragment of the SC where only particular reasoning problems become decidable, but these problems are exactly those that can be important in applications It should not be a surprise for the readers to see that even if an initial theory is an FO2 theory, that is formulated using object variables x and y, we include additional variables (a, for actions, and s, for situations), action terms and situation terms common in the SC.

The Situation Calculus
Description Logics
C2 and Its Relationship to Description Logics
Modeling Dynamical Systems in a Modified Situation Calculus
Reasoning about Actions using Regression
Modified Regression with Lazy Unfolding
Some Computational Complexity Results
A Description-Logic Based Situation Calculus
F ODL both
An Example of Regression in LCsc2
Discussion and Future
ALCQIO(⊔, ⊓, ¬, |, id) and C2 are Equally Expressive
The Correctness of the Modified Regression Operator
ALCO(U ) and F ODL are Equally Expressive
Findings
Restricting Syntax of BATs to Gain Computational Advantages

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.