Hybrid Temporal Situation Calculus for Planning with Continuous Processes

Mikhail Soutchanski

KR-2022 Tutorial @ FLOC-22:

Sunday, July 31st, 2022, 14:00-15:30, 16:00-17:30

Brief Description
Long Description
Length of the Tutorial
Audience and Prerequisites
About this document ...

Brief Description

This tutorial focuses on the representation and semantics of change. The basic language is the situation calculus. This tutorial covers both the well-known logical foundations and the recent developments in the situation calculus. Specifically, the initial part of the tutorial includes logical characterizations of qualitative change within the situation calculus, and the middle part presents a recent approach that extends the previous version of the situation calculus with new representations for reasoning about quantitative change over time. It turns out that this new version of temporal situation calculus can serve as a basis for the development of a new lifted heuristic planner that can solve the planning problems in the mixed discrete-continuous domains. It is “lifted” in a sense that it works with action schemata, but not with instantiated actions. These hybrid domains include not only the usual discrete actions and qualitative properties, but also continuous processes that can be possibly initiated or terminated by actions. The final part of the tutorial includes an overview of the experimental results collected from running a tentative implementation of a new planner on selected benchmarks designed by the planning community for the hybrid domains. Since this tutorial focuses on logical representations and semantics, there will be no discussion of the algorithmic or implementation details related to planning. No previous background in the situation calculus or planning is required. However, it is expected that the attendees have basic understanding of knowledge representation and working knowledge of classical first order logic.

Long Description and Motivation

The situation calculus (SC) is a logical approach to representation and reasoning about actions and their effects. It was proposed in [66,67] to capture common sense reasoning patterns of how the actions and events change properties of the world and mental states of the agents. It was inspired by Isaac Newton's ideas [72], and therefore it described change in terms of fluents and inertia [24]. In particular, it was observed that only the specified fluents change their values from one situation to a new situation, but by default most common sense properties are subject to inertia and remain the same in the new situation. The problem of finding a parsimonious characterization of the inertial properties became known as the frame problem by analogy with the fixed coordinate frame. In contrast to Newton, who described change and inertia in terms of quantitative fluents and their fluxions (derivatives), the original SC approached change in purely qualitative terms [67]. This emphasis on the study of the qualitative aspects of change within SC continued for years, e.g. see [46,41], despite a very productive role that the study of continuous change played in the history of science [15,91]. The research papers about a possible integration within SC of reasoning about qualitative and continuous change started to appear only in the middle of the 1990s, e.g., see [23,70] and the references below.

From the very beginning of Artificial Intelligence (AI), it was recognized that the planning problems at the common sense level can be conveniently formulated in SC as the entailment problem in predicate logic. Cordell Green proposed to solve the (planning) problems using resolution-based theorem proving in situation calculus [42,43,44]. Since his program did not work well [82,16], the subsequent planning research switched to more specialized representations such as STRIPS developed by Richard Fikes and Nils Nilsson [32], and ADL, developed by Edwin Pednault [73]. Accordingly, the semantics of planning has changed. Namely, the planning problem was often reformulated as either the satisfiability problem in propositional logic, or as the reachability problem in an instantiated – propositional level – transition system, where both the initial state and the goal state are specified using fluents with explicitly named constants from the planning instance. In 1999, this historical shift was summarized in [98] as follows: “Despite the early formulation of planning as theorem proving [44], most researchers have long assumed that special-purpose planning algorithms are necessary for practical performance".

However, the knowledge representation research of SC continued, since SC is formulated in a well understood many-sorted first order logic (FOL) with the standard Tarskian semantics [83]. This is in contrast to alternative less expressive approaches to reasoning about action that rely on a non-standard syntax and semantics. In particular, Ray Reiter solved the frame problem on a FOL level in SC [83], and in [84] he provided logical foundations for SC and logical theories for reasoning about actions, events and their effects. He proposed Basic Action Theories (BATs) that include precondition axioms, successor state axioms, initial state axioms, unique name axioms, and the foundational axioms for situations. The latter characterize situations as a (finitely) branching tree with the root in the initial situation [78]. Subsequently, Ray Reiter, Hector Levesque [53], their collaborators and other researchers developed several extensions of SC, including sequential temporal SC [92,75,85,50,51,79,34], SC for reasoning about concurrent actions, reasoning about knowledge [89], a systematic axiomatization of direct and indirect effects of actions [54,59,69,61], reasoning about noisy sensors and effects in SC [4,11], decision-theoretic planning in SC [80,14], and the high level robot control [2,45,90,33]. The foundations of this well-established KR&R research are summarized in the Reiter's book [86,77]. It is explained there that the planning problem can be understood as a special case of the entailment problem in SC within the standard FOL semantics [35,86,16].

In Reiter's SC [86], the change is represented using atemporal fluents, i.e., predicates or functions with situational argument, but without explicit time argument. This is somewhat counter-intuitive, since a large body of knowledge about dynamical systems in science and engineering is formulated in terms of mathematical functions that depend on time explicitly and vary over continuous time. Therefore, it is natural to think about a new temporal SC that can represent changes in hybrid systems, where the actions/events switch between situations, but within each situation the specified quantities can change over time. In hybrid automata [71,1,48,3,26,28], actions or events are responsible for discrete transitions between finitely many atomic states, while states may include processes with continuous evolution over time. However, in some practical applications, e.g., a traffic domain representing a large city with flows of cars moving between intersections [94], or the network of electric power generating stations that feed electricity to large regions [74], a hybrid system is more general than a hybrid automaton. These large scale hybrid systems have relational structure, since their states are no longer atomic, but they can be represented using fluents with object parameters. The Hybrid Temporal SC [8,9], in addition to atemporal fluents that are used to represent qualitatively different contexts, introduces temporal fluents that have an explicit time argument. The latter are suitable to represent continuously varying parameterized processes within a state (context). These new representations facilitate reasoning about the hybrid systems with relational structure. There is an ICAPS-2019 paper [10] demonstrating that this new Hybrid Temporal SC can provide a declarative semantics for PDDL+. PDDL+ is the variant of the Planning Domain Definition Language (PDDL), a standardized language developed to address some concerns related to modelling numeric fluents and durative (continuous) actions in PDDL2.1 [36]. Maria Fox and Derek Long mentioned in [37] that it is desirable to have a purely declarative semantics for PDDL+, and the Hybrid Temporal SC addresses this need.

It turns out that one can develop an efficient lifted heuristic planner for PDDL+ domains using the Hybrid Temporal SC [64]. The shift towards general domain-independent planning algorithms based on heuristic search happened in the end of 1990s, e.g., see [68,12,49,17,47,40]. At the same time and more recently, the researchers gradually realized the importance of lifted planning, i.e., that AI planners can efficiently work with action schemata without constructing beforehand a propositional level transition system, e.g., see [21,25,30,31,93,63,65,18,38,6,39,22,99,13] and other references mentioned there. Moreover, Fangzhen Lin developed and implemented a situation calculus based planner R [55,56] that is a variant of the original STRIPS planning algorithm. His planner R did not use heuristics, but it participated in the international competitions on planning at the common-sense level [56,5]. More recently, [7] considered conformant planning in an open-world setting and developed a situation calculus based planner that relies on progression of local-effect action theories [62], where the initial theory is incomplete, but it has a simple syntactic form [52]. However, to the best of our knowledge, with an exception of [81], SC was never taken as a foundation for designing a lifted heuristic planner. Our provisional implementation [64] has been tested on several benchmarks developed to compare the performance of the state of the art PDDL+ planners such as DiNo [76], SMTPlan [19,20], ENHSP [88,87]. The tutorial will briefly review experimental data collected from our tentative implementation and provide comparison with the state-of-the art in PDDL+ planning.

Length of the Tutorial

The tutorial has a duration of 3 hours on July 31st, 2022: the 1st part is from 14:00-15:30, the 2nd part is from 16:00-17:30.

Audience and Prerequisites

This tutorial focuses on the semantics and logical representation for actions and temporally continuous processes in SC. It is expected that the attendees are not familiar with SC and planning, but they have a basic knowledge of first order logic [29]. All algorithmic and implementation issues will be discussed at another venue. The tutorial will include the following topics.


  1. Introduction to reasoning about action. Intuitive ontology for the situation calculus. Deterministic, primitive, atemporal actions without side-effects [16,53,86,57].
  2. Frame axioms (axioms about lack of effects for actions), the frame problem: Reiter's solution. Effect axioms, normal form for effect axioms. Transforming effect axioms for a given fluent into a single positive effect axiom and a single negative effect axiom for the fluent. Explanation closure, causal completeness, successor state axioms. [83,86]
  3. Foundational axioms for the situation calculus, the tree of situations. Uniform formulas, regressable formulas [78].
  4. Basic Action Theories (BATs): precondition axioms, successor state axioms, initial theory, foundational axioms, unique name axioms (UNA) [78,86]. Closed world assumption (CWA), open world assumption (OWA) [7]. Domain closure assumption (DCA) vs open domains with possibly unspecified objects [35]. State constraints (derived predicates): [54,59]. A compilation approach for acyclic constraints: [69].
  5. The projection and executability problems. A brief review of two techniques for solving these problems: regression (reasoning backwards) [97] and progression (reasoning forward) [95]. Bounded situation calculus theories [27].
  6. Time, instantaneous actions, processes extended in time [86]. The sequential, temporal situation calculus. We discuss (1) new representation that has to be introduced, (2) how the foundational axioms have to be amended, (3) whether we need new axioms.
  7. A recent extension: Hybrid Temporal Situation Calculus (HTSC) [8,9]. Atemporal fluents vs temporal fluents. Continuous processes initiated or terminated by the last action (event). Temporal change axioms (TCA) to represent how temporal numerical fluents continuously change over time in each context. Deriving state evolution axioms (SEA).
  8. Temporal Basic Action Theories in HTSC for sequential actions [8]. Examples. Relation with PDDL+ [10,37].
  9. A lifted heuristic planner based on HTSC [64]. Experimental assessment, and comparison with the other state of the art PDDL+ planners on the challenging benchmarks.
  10. Discussion of possible future research directions.

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Hybrid Temporal Situation Calculus for Planning with Continuous Processes

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