In this paper, we give a case study to show how a high level semantics of processes can be integrated with the event calculus to reason about complex, continuous processes. We present a formal method to specify the semantics of processes in the event calculus and implement the automated reasoning about processes and continuous change in the logical programming framework. Key-words: Reasoning, P...

Extensive research in the field of reasoning about actions and discrete changes led to many different logic-based formalisms such as Action Languages E and C+, Fluent Calculus, Temporal Action Logics, Situation Calculus, and Event Calculus. Some of these formalisms, Situation Calculus and Event Calculus for example, were extended to reason about continuous changes described as functions of time...

Relational semantics for linear logic is a form of non-idempotent intersection type system, from which several informations on the execution of a proof-structure can be recovered. An element of the relational interpretation of a proof-structure R with conclusion Γ acts thus as a type (refining Γ) having R as an inhabitant. We are interested in the following type-checking question: given a proof...

Stochastic differential equations with multiplicative noise need a mathematical prescription due to different interpretations of the stochastic integral. This fact implies specific algorithms to perform numerical integrations or simulations of the stochastic trajectories. Moreover, if the multiplicative noise function is not continuous then the standard algorithms cannot be used. We present an ...

We consider the classical (propositional) version, CBI, of O’Hearn and Pym’s logic of bunched implications (BI) from a modeland proof-theoretic perspective. We make two main contributions in this paper. Firstly, we present a class of algebraic models for CBI which permit the full range of classical multiplicative connectives to be modelled. Our models can be seen as generalisations of Abelian g...

Gentzen’s sequent calculus is a tool to study properties of logics independently of semantics. The main property is cut-elimination which entails the subformula property and consistency. It is also the basis of methods of automated deduction. Although the sequent calculus is very appropriate for classical logic, it raises some concerns in dealing with more refined logics like linear logic. An e...

While difference equations deal with discrete calculus and differential equations with continuous calculus, so-called q-difference equations are considered when studying q-calculus. In this paper, we obtain certain oscillation criteria for second-order q-difference equations, among them a q-calculus version of the famous Kneser theorem. PACS numbers: 02.30.Hq, 02.30.Gp, 02.30.Ks, 02.30.Lt, 02.2...

The paper aims to identify hidden Markov model parameters. unobservable state represents a finite-state jump process. observations contain Wiener noise with state-dependent intensity. identified parameters include the transition intensity matrix of system state, conditional drift and diffusion coefficients in observations. We propose an iterative identification algorithm based on fixed-interval...

<p style='text-indent:20px;'>We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In case multiplicative noise, existence optimal controls and necessary conditions for optimality are derived. additive we obtain a representation gradient cost functional adjoint calculus. The restriction to noise avoids necessity introducing bac...

A theory of differential calculus for nonlinear maps between general locally convex spaces is developed. All convergence notions are topological, and only familiarity with basic results from point set topology, differential calculus in Banach spaces, and locally convex space theory is assumed. The chain rule for continuous kth order differentiability, smoothness of inverse functions, and functi...