Belief, knowledge, lies and other utterances in an algebra for space and extrusion

Abstract

The 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 multiagent 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 $

Symbolic Execution and Reachability Analysis Using Rewriting Modulo SMT for Spatial Concurrent Constraint Systems with Extrusion

“…The spatial concurrent constraint programming with extrusion (SCCP+E) calculus presented in this section follows the developments of [16] and [14]. The syntax of SCCP+E is parametric on an SCSE and it is presented in Definition 4.…”

Declarative Framework for Semantical Interpretations of Structured Information — An Applicative Approach

“…Intuitively, constraint systems build a specific structure of information (that of a poset) and define useful operations between the different elements that make up the totality of the information. Likewise, the notion of computational space and the movement of the information therein may be extended to constraint systems by means of space and extrusion functions [10]. In previous works, formal models describing the concept of space were generally treated from a theoretical standpoint and much of their results are mathematical in nature [6,5].…”

“…Alternatively, we can epistemically interpret these assertions as "agent i believes c" and "agent i believes that agent j believes c" respectively. Movement of information across spaces was introduced by means of the constraint operator ↑ called extrusion [10]. One can now conceive statements like [↑ i [c] j ] i "agent i extrudes the information c to agent j" or epistemically as "agent i extrudes that agent j believes c".…”

Semantic Structures for Spatially-Distributed Multi-Agent Systems

“…One can define a general form of implication by adapting the corresponding notion from Heyting Algebras to cs. A Heyting implication c → d in our setting corresponds to the weakest constraint one needs to join c with to derive d. [8]). A constraint system (Con, ⊑) is said to be a constraint frame iff its joins distribute over arbitrary meets.…”