System BV is an extension of multiplicative linear logic with a non-commutative self-dual operator. We first map derivations of system BV of the calculus of structures to rewritings in a term rewriting system modulo equality, and then express this rewriting system as a Maude system module. This results in an automated proof search implementation for this system, and provides a recipe for implementing existing calculus of structures systems for other logics. Our result is interesting from the view of applications, specially, where sequentiality is essential, e.g., planning and natural language processing. In particular, we argue that we can express plans as logical formulae by using the sequential operator of BV and reason on them in a purely logical way.

The Fluent Calculus is presented as a comprehensive specification and programming language for endowing robots with the ability of task planning in complex environments. Based on a solution to the classical Frame Problem in pure first-order logic, our calculus allows to solve planning problems where the robot has incomplete state knowledge and which involve the use of sensors, actions with uncertain effects, actions with ramications (i.e., indirect effects), and the concurrent execution of actions. Our new theory of sensing is distinguished by its simple inference scheme for calculating the effects of actions on state knowledge and by its comparatively simple account of non-knowledge. A realization of the Fluent Calculus by means of constraint logic programming is presented. Outstanding novel features of the system are to solve the inferential Frame Problem under incomplete state information, to allow for solving planning problems with knowledge goals, and to combine nondeterminism, concurrency, and ramification.

We present a purely logical framework to planning where we bring the sequential and parallel composition in the plans to the same level, as in process algebras. The problem of expressing causality, which is very challenging for common logics and traditional deductive systems, is solved by resorting to a recently developed extension of multiplicative exponential linear logic with a self-dual, noncommutative operator. We present an encoding of the conjunctive planning problems in this logic, and provide a constructive soundness and completeness result. We argue that this work is the first, but crucial, step of a uniform deductive formalism that connects planning and concurrency inside a common language, and allows to transfer methods from concurrency to planning.

Successor state axioms are an optimal solution to the famous Frame Problem in reasoning about actions---but only as far as its representational aspect is concerned. We show how by gradually applying the principle of reification to these axioms, one can achieve gradual improvement regarding the inferential aspect without losing the representational merits. The resulting concept of state update axioms constitutes a novel version of what is known as the Fluent Calculus. We illustrate that under the provision that actions have no so-called open e#ects, any Situation Calculus specification can be transformed into an essentially equivalent Fluent Calculus specification, in which at the same time the representational and the inferential aspect of the Frame Problem are addressed.

Labelled event structures is a model of concurrency, where causality between actions is expressed by a partial order and the nondeterminism is expressed by a conflict relation on actions. We present a new approach to linear logic planning where computation is performed as cutfree proof search. We provide a labelled event structure semantics for the planning problems, and establish an explicit correspondence between the cut-free proofs of the planning problems and partial order plans that we extract from proofs. This results in a concurrency theoretic semantics of planning problems. As the underlying formalism, we employ the recently developed calculus of structures. This way, additional proof theoretical properties, that are not available in the sequent calculus presentation of linear logic, become available. We provide an implementation of our approach, and argue that this work is a crucial step for using the methods of concurrency for establishing a meaningful notion of plan equivalence.

System NEL is a conservative extension of multiplicative exponential linear logic with a self-dual, non-commutative operator. In this paper, we express plans as logical formulae by using this sequential operator.

We present an approach to linear logic planning where an explicit correspondence between partial order plans and multiplicative exponential linear logic proofs is established. This is performed by extracting partial order plans from sound and complete encodings of planning problems in multiplicative exponential linear logic in a way that exhibits a non-interleaving behavioral concurrency semantics. Relying on this fact, we argue that this work is a crucial step for establishing a common language for concurrency and planning that will allow to carry techniques and methods between these two fields.

We present a framework in which partial order plans are used for project management tasks where the dependency between each sub task and employee can be observed. For this purpose, extending the resource conscious linear logic planning, we establish an explicit correspondence between multiplicative exponential linear logic proofs and partial order plans. We express planning problems as formulae, and then extract partial order plans from the proofs of these formulae. We provide a constructive soundness and completeness result and show how this approach to planning can be used for project management.

We describe a new formalisation in Isabelle/HOL of Intuitionistic Linear Logic and consider the support this provides for constructing plans by proving the achievability of given planning goals. The plans so found are provably correct, by construction. This representation of plans in linear logic provides a concise account of planning with sensing actions, allows the creation and deletion of objects, and solves the frame problem in an elegant way. Within this setting, we show how planning algorithms are implemented as search strategies within a theorem proving system. This allows us to provide a flexible methodology for developing search strategies that is independent of soundness issues. This feature is illustrated in two ways. Firstly, following ideas from logic programming, we show how a significant symmetry in search, caused by context splitting, can be pruned by using a derived inference rule. Secondly, we show how domain specific constraints on synthesis are supported and how they can be used to find contingent or conformant plans. We illustrate the approach with example planning scenarios. 1.