On the Expressiveness of Spatial Constraint Systems

In this paper we shall report on our progress using spatial constraint system as an abstract representation of modal and epistemic behaviour. First we shall give an introduction as well as the background to our work. Then, we present our preliminary results on the representation of modal behaviour by using spatial constraint systems. Then, we present our ongoing work on the characterization of the epistemic notion of knowledge. Finally, we discuss about the future work of our research

An Algebraic View of Space/Belief and Extrusion/Utterance for Concurrency/Epistemic Logic

International audienceWe enrich spatial constraint systems with operators to specify information and processes moving from a space to another. We shall refer to these news structures as spatial constraint systems with extrusion. We shall investigate the properties of this new family of constraint systems and illustrate their applications. From a computational point of view the new operators provide for pro-cess/information extrusion, a central concept in formalisms for mobile communication. From an epistemic point of view extrusion corresponds to a notion we shall call utterance; a piece of information that an agent communicates to others but that may be inconsistent with the agent's beliefs. Utterances can then be used to express instances of epistemic notions, which are common place in social media, such as hoaxes or intentional lies. Spatial constraint systems with extrusion can be seen as complete Heyting algebras equipped with maps to account for spatial and epistemic specification

Belief, Knowledge, Lies and Other Utterances in an Algebra for Space and Extrusion

International audienceThe notion of constraint system (cs) is central to declarative formalisms from concurrency theory such as process calculi for concurrent constraint programming (ccp). Constraint systems are often represented as lattices: their elements, called constraints, represent partial information and their order corresponds to entailment. Recently a notion of n-agent spatial cs was introduced to represent information in concurrent constraint programs for spatially distributed multi-agent systems. From a computational point of view a spatial constraint system can be used to specify partial information holding in a given agent's space (local information). From an epistemic point of view a spatial cs can be used to specify information that a given agent considers true (beliefs). Spatial constraint systems, however, do not provide a mechanism for specifying the mobility of information/processes from one space to another. Information mobility is a fundamental aspect of concurrent systems. In this article we develop the theory of spatial constraint systems with operators to specify information and processes moving from a space to another. We shall investigate the properties of this new family of constraint systems and illustrate their applications. From a computational point of view the new operators provide for process/information extrusion, a central concept in formalisms for mobile communication. From an epistemic point of view extrusion corresponds I to a notion we shall call utterance; a piece of information that an agent communicate to others but that may be inconsistent with the agent's beliefs. Utterances can then be used to express instances of epistemic notions such as hoaxes or intentional lies which are common place in social media. Spatial constraint system can express the epistemic notion of belief by means of space functions that specify local information. We shall also show that spatial constraint can also express the epistemic notion of knowledge by means of a derived spatial operator that specifies global information

Deriving Inverse Operators for Modal Logic

International audienceSpatial constraint systems are algebraic structures from concurrent constraint programming to specify spatial and epistemic behavior in multi-agent systems. We shall use spatial constraint systems to give an abstract characterization of the notion of normality in modal logic and to derive right inverse/reverse operators for modal languages. In particular, we shall identify the weakest condition for the existence of right inverses and show that the abstract notion of normality corresponds to the preservation of finite suprema. We shall apply our results to existing modal languages such as the weakest normal modal logic, Hennessy-Milner logic, and linear-time temporal logic. We shall discuss our results in the context of modal concepts such as bisimilarity and inconsistency invariance

A Substructural Epistemic Resource Logic: Theory and Modelling Applications

We present a substructural epistemic logic, based on Boolean BI, in which the epistemic modalities are parametrized on agents' local resources. The new modalities can be seen as generalizations of the usual epistemic modalities. The logic combines Boolean BI's resource semantics --- we introduce BI and its resource semantics at some length --- with epistemic agency. We illustrate the use of the logic in systems modelling by discussing some examples about access control, including semaphores, using resource tokens. We also give a labelled tableaux calculus and establish soundness and completeness with respect to the resource semantics

Verification of Spatial and Temporal Modalities in Biochemical Systems

AbstractBiochemical systems such as metabolic and signaling pathways tend to be arranged in a physical space: the product of one reaction must be in the right place to become the reactant for the subsequent reaction in the pathway. Moreover, in some cases, the behavior of the systems can depend on both, the location of the reactants as well as on the time needed for the reaction to occur. We address the problem of specifying and verifying properties of biochemical systems that exhibit both temporal and spatial modalities at the same time. For that, we use as specification language a fragment of intuitionistic linear logic with subexponentials (SELL). The subexponential signature allows us to capture the spatial relations among the different components of the system and the timed constraints for reactions to occur. We show that our framework is general enough to give a declarative semantics to P-Systems and we show that such logical characterization has a strong level of adequacy. Hence, derivations in SELL follow exactly the behavior of the modeled system

Weighted logics for artificial intelligence : an introductory discussion

International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas