Reasoning about actions with Temporal Answer Sets

Abstract

In this paper, we combine Answer Set Programming (ASP) with Dynamic Linear Time Temporal Logic (DLTL) to define a temporal logic programming language for reasoning about complex actions and infinite computations. DLTL extends propositional temporal logic of linear time with regular programs of propositional dynamic logic, which are used for indexing temporal modalities. The action language allows general DLTL formulas to be included in domain descriptions to constrain the space of possible extensions. We introduce a notion of Temporal Answer Set for domain descriptions, based on the usual notion of Answer Set. Also, we provide a translation of domain descriptions into standard ASP and we use Bounded Model Checking techniques for the verification of DLTL constraints.

Achieving completeness in the verification of action theories by Bounded Model Checking in ASP

“…The language is also well suited to describe causal dependencies among fluents [26] by the definition of static and dynamic causal laws similar to the ones in the action languages K [15] and C + [27].…”

“…In this paper, we start from the temporal action theories introduced in [26], formulated in a temporal extension of answer set programming (ASP [18]) based on Dynamic Linear Time Temporal Logic (DLTL [31]) and we exploit Bounded Model Checking (BMC) techniques for the verification of properties of such action theories. BMC [7] is an efficient model checking technique which does not require a tableau or automaton construction.…”

“…Since ASP naturally accommodates for reasoning about actions, in [26] this encoding is extended to DLTL formulas, for reasoning about theories including complex actions and programs. These papers do not address the problem of achieving completeness.…”

“…Unlike [30,26], the search for a counterexample exploits the Büchi automaton construction [21] as well as the transition system. Unlike [10], a "counterexample" path is searched for, without assuming that the Büchi automaton is constructed in advance.…”

“…As in [26], verification is performed on a transition system provided by a domain description in a temporal action theory, and our BMC approach is used for proving properties of domain descriptions. The action theory is given in a temporal extension of ASP, based on the generalization of the notion of answer set [18] to temporal answer sets.…”