Similarity and bisimilarity notions appropriate for characterizing indistinguishability in fragments of the calculus of relations

Motivated by applications in databases, this paper considers various fragments of the calculus of binary relations. The fragments are obtained by leaving out, or keeping in, some of the standard operators, along with some derived operators such as set difference, projection, coprojection, and residuation. For each considered fragment, a characterization is obtained for when two given binary relational structures are indistinguishable by expressions in that fragment. The characterizations are based on appropriately adapted notions of simulation and bisimulation.Comment: 36 pages, Journal of Logic and Computation 201

A hybrid dynamic logic for event/data-based systems

We propose E↓ -logic as a formal foundation for the specification and development of event-based systems with local data states. The logic is intended to cover a broad range of abstraction levels from abstract requirements specifications up to constructive specifications. Our logic uses diamond and box modalities over structured actions adopted from dynamic logic. Atomic actions are pairs Open image in new window where e is an event and /ψ a state transition predicate capturing the allowed reactions to the event. To write concrete specifications of recursive process structures we integrate (control) state variables and binders of hybrid logic. The semantic interpretation relies on event/data transition systems; specification refinement is defined by model class inclusion. For the presentation of constructive specifications we propose operational event/data specifications allowing for familiar, diagrammatic representations by state transition graphs. We show that E↓-logic is powerful enough to characterise the semantics of an operational specification by a single E↓-sentence. Thus the whole development process can rely on E↓-logic and its semantics as a common basis. This includes also a variety of implementation constructors to support, among others, event refinement and parallel composition.publishe

The Philosophical Foundations of PLEN: A Protocol-theoretic Logic of Epistemic Norms

In this dissertation, I defend the protocol-theoretic account of epistemic norms. The protocol-theoretic account amounts to three theses: (i) There are norms of epistemic rationality that are procedural; epistemic rationality is at least partially defined by rules that restrict the possible ways in which epistemic actions and processes can be sequenced, combined, or chosen among under varying conditions. (ii) Epistemic rationality is ineliminably defined by procedural norms; procedural restrictions provide an irreducible unifying structure for even apparently non-procedural prescriptions and normative expressions, and they are practically indispensable in our cognitive lives. (iii) These procedural epistemic norms are best analyzed in terms of the protocol (or program) constructions of dynamic logic. I defend (i) and (ii) at length and in multi-faceted ways, and I argue that they entail a set of criteria of adequacy for models of epistemic dynamics and abstract accounts of epistemic norms. I then define PLEN, the protocol-theoretic logic of epistemic norms. PLEN is a dynamic logic that analyzes epistemic rationality norms with protocol constructions interpreted over multi-graph based models of epistemic dynamics. The kernel of the overall argument of the dissertation is showing that PLEN uniquely satisfies the criteria defended; none of the familiar, rival frameworks for modeling epistemic dynamics or normative concepts are capable of satisfying these criteria to the same degree as PLEN. The overarching argument of the dissertation is thus a theory-preference argument for PLEN