Abstract Though Propositional Dynamic Logic (PDL) as well as its relation to planning has been widely studied, there is as of yet no consensus as to how to handle parallelism in the framework. In this paper, we propose a parallel version of the Dynamic Logic of Propositional Assignments (${\textsf{DL-PA} } $), a simple fragment of PDL in which atomic programs are assignments of the truth value of a formula to a propositional variable. We introduce two new operators for ${\textsf{DL-PA} }$, namely parallel composition and inclusive non-deterministic composition. For the former, we suppose that two programs can be executed in parallel if they do not assign different values to the same variable. We give a polynomial translation of the resulting Dynamic Logic of Parallel Propositional Assignments (${\textsf{DL-PPA} }$) into ${\textsf{DL-PA} }$, thereby showing that complexity remains in PSpace. We then turn to planning and show how to capture executability of parallel STRIPS-like actions and solvability of planning tasks by parallel plans in ${\textsf{DL-PPA} }$, following three different semantics for parallelism: one closely following our criterion for parallelism in ${\textsf{DL-PPA} }$, and two from the literature based on interleaving.

We extend belief revision theory from propositional logic to the modal logic S5. Our first contribution takes the form of three new postulates (M1-M3) that go beyond the AGM ones and capture the idea of minimal change in the presence of modalities. Concerning the construction of modal revision operations, we work with set pseudo-distances, i.e., distances between sets of points that may violate the triangle-inequality. Our second contribution is the identification of three axioms (A3-A5) that go beyond the standard axioms of metrics. Loosely speaking, our main result states the following: if a pseudo-distance satisfies certain axioms, then the induced revision operation satisfies (M1-M3). We investigate three pseudo-distances from the literature (Dhaus, Dinj, Dsum), and the three induced revision operations (*Haus, *Inj, *Sum). Using our main result, we show that only *Sum satisfies (M1-M3) all together. As a last contribution, we revisit a major criticism of AGM operations, namely that the revisions of (p ∧ q) and (p ∧ (p → q)) are identical. We show that the problem disappears if instead of material implication we use the modal operator of strict implication that can be defined in S5.

In the logic of theory change, the AGM model has acquired the status of a standard model. However, the AGM model does not seem adequate for some contexts and application domains. This inspired many researchers to propose extensions and generalizations to AGM. Among these extensions, one of the most important are belief bases. Belief bases have more expressivity than belief sets, as explicit and implicit beliefs have different statuses. In this paper, we present reformulation, a belief change operation that allows us to reformulate a belief base making some particular sentences explicit without modifying the consequences of the belief base. We provide a constructive method and its axiomatic characterization.

Epistemic planning is useful in situations where multiple agents have different knowledge and beliefs about the world, such as in robot-human interaction. One aspect that has been largely neglected in the literature is planning with observations in the presence of false beliefs. This is a particularly challenging problem because it requires belief revision. We introduce a simple specification language for reasoning about actions with knowledge and belief. We demonstrate our approach on well-known false-belief tasks such as the Sally-Anne Task and compare it to other action languages. Our logic leads to an epistemic planning formalism that is expressive enough to model second-order false-belief tasks, yet has the same computational complexity as classical planning.

Analogical proportions are statements of the form “α is to β as γ is to δ”, noted α:β::γ:δ, and can be understood as “α differs from β as γ differs from δ” and conversely “β differs from α as δ differs from γ”. In this paper, α, β, γ, δ are supposed to be propositional logic formulas, which are appropriate for representing concepts. There exists one approach, developed over the last 15 years, where “α differs from β” is understood in terms of the negation of the material implication α → β. The paper investigates another view where “α differs from β” is interpreted in terms of transformations where some variables become false, some variables become true, and some variables become irrelevant. Both approaches satisfy the three basic postulates of analogical proportions (reflexivity, symmetry, and stability under central permutation), as well as other interesting properties such as transitivity and unicity of δ such that α:β::γ:δ. However, the two approaches depart from each other since they do not validate the same analogical proportions. In particular, when p,q,r are atoms the proportion p:(p∧r)::q:(q∧r) holds in the new approach, while it fails to do so for the other. The new approach exhibits also a good behaviour with respect to integrity constraints. It is advocated that this makes it appropriate for handling analogy between concepts, while the other approach has proved to be fruitful for Boolean features-based representations. The paper provides a thorough analysis of the differences between the two approaches.

Conditional logics are usually interpreted in terms of closest world and minimal change. It relies on a measure of distance between worlds which is defined abstractly, i.e. as an element of the model. The typical example of a concrete measure in literature is the Hamming distance. We show that given countably infinite atomic propositions in the language, Hamming distance is not merely an example, but grounded for two arguably most important conditional logics, Lewis' VC and VCU. That means, a formula is satisfied in a VC (resp. VCU) model, if and only if it is satisfied in a VC (resp. VCU) model whose distance between worlds is Hammingian.

Abstract Dynamics and uncertainty are essential features of real-life argumentation, and many recent studies have focused on integrating both aspects into Dung’s well-known abstract argumentation frameworks (AFs). This paper proposes a combination of the two lines of research through a well-behaved logical tool: dynamic logic of propositional assignments (DL-PA). Our results show that the main reasoning tasks of virtually all existing formalisms qualitatively representing uncertainty about AFs are encodable in DL-PA. Moreover, the same tool is also useful for capturing dynamic structures, such as control AFs, as well as for developing more refined forms of argumentative communication under uncertainty.

We introduce a simple model of agency that is based on the concepts of control and attempt. Both relate agents and propositional variables. Moreover, they can be nested: an agent i may control whether another agent j controls a propositional variable p; i may control whether j attempts to change p; i may attempt to change whether j controls p; i may attempt to change whether j attempts to change p; and so on. In this framework we define several modal operators of time and agency: the LTL operators on the one hand, and the Chellas and the deliberative stit operator on the other. While in the standard stit framework the model checking problem is unfeasible because its models are infinite, in our framework models are represented in a finite and compact way: they are grounded on the primitive concepts of control and attempt. This makes model checking practically feasible. We prove its PSPACE-completeness and we show how the concept of social influence can be captured.

We introduce a multi-agent, dynamic extension of abstract argumentation frameworks (AFs), strongly inspired by epistemic logic, where agents have only partial information about the conflicts between arguments. These frameworks can be used to model a variety of situations. For instance, those in which agents have bounded logical resources and therefore fail to spot some of the actual attacks, or those where some arguments are not explicitly and fully stated (enthymematic argumentation). Moreover, we include second-order knowledge and common knowledge of the attack relation in our structures (where the latter accounts for the state of the debate), so as to reason about different kinds of persuasion and about strategic features. This version of multi-agent AFs, as well as their updates with public announcements of attacks (more concretely, the effects of these updates on the acceptability of an argument) can be described using S5-PAL, a well-known dynamic-epistemic logic. We also discuss how to extend our proposal to capture arbitrary higher-order attitudes and uncertainty.

Existing dynamic epistemic logics combine standard epistemic logic with a restricted version of dynamic logic. Instead, we here combine a restricted epistemic logic with a rich version of dynamic logic. The epistemic logic is based on `knowing-whether' operators and basically disallows disjunctions and conjunctions in their scope; it moreover captures `knowing-what'. The dynamic logic has not only all the standard program operators of Propositional Dynamic Logic, but also parallel composition as well as an operator of inclusive nondeterministic composition; its atomic programs are assignments of propositional variables. We show that the resulting dynamic epistemic logic is powerful enough to capture several kinds of sequential and parallel planning, and so both in the unbounded and in the finite horizon version.

We study the relation between two existing formalisms: incomplete argumentation frameworks (IAFs) and epistemic logic of visibility (ELV). We show that the set of completions of a given IAF naturally corresponds to a specific equivalence class of possible worlds within the model of visibility. This connection is further strengthened in two directions. First, we show how to reduce argument acceptance problems of IAFs to ELV model-checking problems. Second, we highlight the epistemic assumptions that underlie IAFs by providing a minimal epistemic logic for IAFs.

Hierarchical Task Network (HTN) planning is showing its power in real-world planning. Although domain experts have partial hierarchical domain knowledge, it is time-consuming to specify all HTN methods, leaving them incomplete. On the other hand, traditional HTN learning approaches focus only on declarative goals, omitting the hierarchical domain knowledge. In this paper, we propose a novel learning framework to refine HTN methods via task insertion with completely preserving the original methods. As it is difficult to identify incomplete methods without designating declarative goals for compound tasks, we introduce the notion of prioritized preference to capture the incompleteness possibility of methods. Specifically, the framework first computes the preferred completion profile w.r.t. the prioritized preference to refine the incomplete methods. Then it finds the minimal set of refined methods via a method substitution operation. Experimental analysis demonstrates that our approach is effective, especially in solving new HTN planning instances.

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This work deals with logical formalization and problem solving using automated solvers. We present the automatic translator TouIST that provides a simple language to generate logical formulas from a problem description. Our tool allows us to model many static or dynamic combinatorial problems and to benefit from the regular improvements of SAT, QBF or SMT solvers in order to solve these problems efficiently. In particular, we show how to use TouIST to solve different classes of planning tasks in Artificial Intelligence.

We study a simple version of multi-agent epistemic planning where the number of parallel steps has to be minimized. We prove that this extension of classical planning is in PSPACE. We propose an encoding in PDDL and present some experiments providing evidence that this encoding allows us to solve practical problems. The types of problems we can encode include problems in which one agent can teach another agent how to perform a task and communication problems where some information must not be revealed to some agents.

Evidence logics model agents' belief revision process as they incorporate and aggregate information obtained from multiple sources. This information is captured using neighbourhood structures, where individual neighbourhoods represent pieces of evidence. In this paper we propose an extended framework which allows one to explicitly quantify either the number of evidence sets, or effort, needed to justify a given proposition, provide a complete deductive calculus and a proof of decidability, and show how existing frameworks can be embedded into ours.

We introduce a dynamic logic with parallel composition and two kinds of nondeterministic composition, exclusive and inclusive. We show PSPACE completeness of both the model checking and the satisfiability problem and apply our logic to sequential and parallel classical planning where actions have conditional effects.

Active integrity constraints have been introduced in the database community as a way to restore integrity based on a set of preferred update actions. We view active integrity constraints as dynamic logic programs and show how several semantics of database repair that were proposed in the literature can be characterised in Dynamic Logic of Propositional Assignments DL-PA . We moreover propose a new definition of repair which makes use of the programs of Dynamic Logic to provide repair solutions based on an iterating procedure. After an analysis of their properties and a comparison to the previous approaches, we provide complexity results for the problem of existence of these new repairs. Furthermore, an extension on databases with history is explored and the behavior of the various repairs is adjusted to work in this setting. For all these definitions we provide DL-PA counterparts of reasoning and decision problems, such as the existence of a repair or the existence of a unique repair.

Judgment aggregation models a group of agents having to collectively decide over a number of logically interconnected issues starting from their individual opinions. In recent years, a growing literature has focused on the design of logical systems for social choice theory, and for judgment aggregation in particular, making use of logical languages designed ad hoc for this purpose. In this paper we deploy the existing formalism of Dynamic Logic of Propositional Assignments (DL-PA), an instance of Propositional Dynamic Logic where atomic programs affect propositional valuations. We show that DL-PA is a well-suited formalism for modeling the aggregation of binary judgments from multiple agents, by providing logical equivalences in DL-PA for some of the best-known aggregation procedures, desirable axioms coming from the literature on judgment aggregation and properties for the safety of the agenda problem.

We introduce a first-order extension of dynamic logic (FO-DL), suitable to represent and reason about the behaviour of Data-aware Systems (DaS), which are systems whose data content is explicitly exhibited in the system’s description. We illustrate the expressivity of the formal framework by modelling English auctions as DaS, and by specifying relevant properties in FO-DL. Most importantly, we develop an abstraction-based verification procedure, thus proving that the model checking problem for DaS against FO-DL is actually decidable, provided some mild assumptions on the interpretationdomain.

In this paper, we propose a single-agent logic of goal-directed knowing how extending the standard epistemic logic of knowing that with a new knowing how operator. The semantics of the new operator is based on the idea that knowing how to achieve phi means that there exists a (uniform) strategy such that the agent knows that it can make sure phi. We give an intuitive axiomatisation of our logic and prove the soundness, completeness, and decidability of the logic. The crucial axioms relating knowing that and knowing how illustrate our understanding of knowing how in this setting. This logic can be used in representing and reasoning about knowledge-how.

In this paper we attempt to shed light on the concept of an agent’s knowledge after a non-deterministic action is executed. We start by making a comparison between notions of non-deterministic choice, and between notions of sequential composition, of settings with dynamic and/or epistemic character; namely Propositional Dynamic Logic (PDL), Dynamic Epistemic Logic (DEL), and the more recent logic of Semi-Public Environments (SPE). These logics represent two different approaches for defining the aforementioned actions, and in order to provide unified frameworks that encompass both, we define the logics DELVO (DEL+Vision+Ontic change) and PDLVE (PDL+Vision+Epistemic operators). DELVO is given a sound and complete axiomatisation.

We extend hierarchical task network planning with task insertion (TIHTN) by introducing state constraints, called TIHTNS. We show that just as for TIHTN planning, all solutions of the TIHTNS planning problem can be obtained by acyclic decomposition and task insertion, entailing that its plan-existence problem is decidable without any restriction on decomposition methods. We also prove that the extension by state constraints does not increase the complexity of the plan-existence problem, which stays 2-NEXPTIME-complete, based on an acyclic progression operator. In addition, we show that TIHTNS planning covers not only the original TIHTN planning but also hierarchy-relaxed hierarchical goal network planning.

A realistic model of multi-agent planning must allow us to formalize notions which are absent in classical planning, such as communication and knowledge. We investigate multi-agent planning based on a simple logic of knowledge that is grounded on the visibility of propositional variables. Using such a formal logic allows us to prove the existence of a plan given the description of the individual actions. We present an encoding of multi-agent planning problems expressed in this logic into the standard planning language PDDL. The solvability of a planning task is reduced to a model checking problem in a dynamic extension of our logic, proving its complexity. Feeding the resulting problem into a PDDL planner provides a provably correct plan for the original multi-agent planning problem. We apply our method on several examples such as the gossip problem.

The gossip problem, in which information (secrets) must be shared among a certain number of agents using the minimum number of calls, is of interest in the conception of communication networks and protocols. We extend the gossip problem to arbitrary epistemic depths. For example, we may require not only that all agents know all secrets but also that all agents know that all agents know all secrets. We give optimal protocols for the generalised gossip problem, in the case of two-way communications, one-way communications and parallel communication. In the presence of negative goals testing the existence of a successful protocol is NP-complete.

When a planning task cannot be solved then it can often be made solvable by modifying it a bit: one may change either the set of actions, or the initial state, or the goal description. We show that modification of actions can be reduced to initial state modification. We then apply Katsuno and Mendelzon's distinction between update and revision and show that the modification of the initial state is an update and the modification of the goal description is a revision. We consider variants of Forbus's update and Dalal's revision operation and argue that existing belief change operations do not apply as they stand because their inputs are boolean formulas, while plan task modification involves counterfactual statements. We show that they can be captured in Dynamic Logic of Propositional Assignments DL-PA.

A service oriented architecture (SOA) enables cooperation in an open and highly concurrent context. In this paper, we investigate the management of personal information by an SOA service consumer while invoking composed services. Generally speaking, managing personal information relates to different aspects of data management (mainly storage, persistence and querying). In this work, we focus on privacy and confidentiality in a business to user (b2u) application and on critical information dissemination in business to business (b2b) solutions. For these applications, we study the balance between quality of service (that works better when provided with our personal data) and the consumer's data access policy. We present a service architecture that is based on an open multi-agent system where agents provide and invoke (composed) services in order to achieve their goals. We describe a logic-based trust module that a service consumer can use to assess his trust toward composed services (which are perceived as composed actions executed by a group of agents in the system). Our trust module, using an abduction mechanism, provides the service consumer with a synthesized view of his beliefs about the current state of the multi-agent system. This view is coupled with an answer to the question: why should I trust or not this composition? We then illustrate our solution in a case study involving a professional social network (like linkedin, viadeo, etc.). We discusses how the CEO of a start-up company collects information about a potential recruit, while preserving his personal information (because he might have to provide some when collecting information), using composed services provided by the members of the network including the recruit herself.

We study a version of Propositional Dynamic Logic (PDL) that we call Dynamic Logic of Propositional Assignments (DL-PA). The atomic programs of DL-PA are assignments of propositional variables to true or to false. We show that DL-PA behaves better than PDL, having e.g. compactness and eliminability of the Kleene star. We establish tight complexity results: both satisfiability and model checking are EXPTIME-complete.

We present and study a general family of belief update operators in a propositional setting. Its operators are based on formula/ literal dependence, which is more fine-grained than the notion of formula/ variable dependence that was proposed in the literature: formula/variable dependence is a particular case of formula/literal dependence. Our update operators are defined according to the “forget-then-conjoin” scheme: updating a belief base by an input formula consists in first forgetting in the base every literal on which the input formula has a negative influence, and then conjoining the resulting base with the input formula. The operators of our family differ by the underlying notion of formula/literal dependence, which may be defined syntactically or semantically, and which may or may not exploit further information like known persistent literals and pre-set dependencies. We argue that this allows to handle the frame problem and the ramification problem in a more appropriate way. We evaluate the update operators of our family w.r.t. two important dimensions: the logical dimension, by checking the status of the Katsuno-Mendelzon postulates for update, and the computational dimension, by identifying the complexity of a number of decision problems (including model checking, consistency and inference), both in the general case and in some restricted cases, as well as by studying compactability issues. It follows that several operators of our family are interesting alternatives to previous belief update operators.

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Public announcement logic extends multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. In this article, we propose a labelled tableau calculus for this logic, and show that it decides satisfiability of formulas in deterministic polynomial space. Since this problem is known to be PSPACE-complete, it follows that our proof method is optimal.

In the recent years, several formal approaches to the specification of normative multi-agent systems (MASs) and artificial institutions have been proposed. The aim of this article is to advance the state of the art in this area by proposing an approach in which a normative MAS is conceived to be autonomous, in the sense that it is able to create, maintain and eventually change its own institutions by itself, without the intervention of an external designer in this process. In our approach the existence and the dynamics of an institution (norms, rules, institutional facts, etc.) are determined by the (individual and collective) acceptances of its members, and its dynamics depends on the dynamics of these acceptances. In order to meet this objective, we propose the logic 𝒜ℒ (Acceptance Logic) in which the acceptance of a proposition by the agents qua members of an institution is introduced. Such propositions are true w.r.t. an institutional context and correspond to facts that are instituted in an attitude-dependent way. The second part of the article is devoted to the logical characterization of some important notions in the theory of institutions. We provide a formalization of the concept of constitutive rule, expressed by a statement of the form ‘X counts as Y in the context of institution x’. Then, we formalize the concepts of obligation and permission (so called regulative rules). In our approach, constitutive rules and regulative rules of a certain institution are attitude-dependent facts which are grounded on the acceptances of the members of the institution.

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Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: □φ expresses that φ is true after an arbitrary announcement ψ. As this includes the trivial announcement ⊤, one might as well say that □φ expresses what remains true after any announcement: it therefore corresponds to truth persistence after (definable) relativisation. The dual operation ⋄φ expresses that there is an announcement after which φ. This gives a perspective on Fitch's knowability issues: for which formulas φ does it hold that φ → ⋄Kφ? We give various semantic results, and we show completeness for a Hilbert-style axiomatisation of this logic.

In this paper we show how coalition logic can be reduced to the fusion of a normal modal STIT logic for agency and a standard normal temporal logic for discrete time, and how this multi-modal system can be suitably extended with an epistemic modality. Both systems are complete, and we provide a new axiomatization for the STIT-fragment. The epistemic extension enables us to express that agents see to something under uncertainty about the present state or uncertainty about which action is being taken. In accordance with established terminology in the planning community, we call this version of STIT the 'conformant STIT'. The conformant STIT enables us to express that agents are able to perform a uniform strategy. As a final word of recommendation for this paper we want to point out that its subject is at the junction of four academic fields, viz. modal logic, philosophy, game-theory and AI-planning.

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We present the basic framework of a logic of actions and plans defined in terms of modal logic combined with a notion of dependence. The latter is used as a weak causal connection between actions and literals. In this paper we focus on the frame problem and demonstrate how it can be solved in our framework in a simple and monotonic way. We give the semantics, and associate an axiomatics and a decision procedure to it. The decision procedure is based on a sound and complete tableau method with single step rules to treat dependence. We show how it can be used to generate plans. Our solution is formally assessed by a translation of Gelfond and Lifschitz' logic A. We briefly sketch the second part of the paper, showing how we can go beyond A by some examples involving nondeterminism and ramifications.

In this paper we generalize the existing tableau methods for modal logics. First of all, while usual modal tableaux are based on trees, our basic structures are rooted directed acyclic graphs (RDAG). This allows natural tableau rules for some modal logics that are difficult to capture in the usual way (such as those having an accessibility relation that is dense or confluent). Second, tableau rules rewrite patterns, which are (schemas of) parts of a RDAG. A particular case of these rules are the single-step rules recently proposed by Massacci. This allows in particular tableau rule presentations for K5, KD5, K45, KD45, and S5 that respect the subformula property. Third, we divide modal tableau rules into propagation rules and structural rules. Structural rules construct new edges and nodes (without adding formulas to nodes), while propagation rules add formulas to nodes. This distinction allows to prove completeness in a modular way.

We investigate the notion of interference between formulas as a basis for change operations. Such a notion permits us to enrich conditional logics with a frame axiom. This new logic allows us to solve in a natural way some of the problems appearing in the model based approach to change. © 1994 John Wiley & Sons, Inc.