Tool support for reasoning in display calculi

We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error prone. As an example, we implement the display calculus D.EAK of dynamic epistemic logic. Second, we provide embeddings of the calculus in the theorem prover Isabelle for formalising proofs about D.EAK. As a case study we show that the solution of the muddy children puzzle is derivable for any number of muddy children. Third, there is a set of meta-tools, that allows us to adapt the tool for a wide variety of user defined calculi

A Cyclic Proof System for Full Computation Tree Logic

Full Computation Tree Logic, commonly denoted CTL*, is the extension of Linear Temporal Logic LTL by path quantification for reasoning about branching time. In contrast to traditional Computation Tree Logic CTL, the path quantifiers are not bound to specific linear modalities, resulting in a more expressive language. We present a sound and complete hypersequent calculus for CTL*. The proof system is cyclic in the sense that proofs are finite derivation trees with back-edges. A syntactic success condition on non-axiomatic leaves guarantees soundness. Completeness is established by relating cyclic proofs to a natural ill-founded sequent calculus for the logic

Infinets: The parallel syntax for non-wellfounded proof-theory

International audienceLogics based on the µ-calculus are used to model inductive and coinductive reasoning and to verify reactive systems. A well-structured proof-theory is needed in order to apply such logics to the study of programming languages with (co)inductive data types and automated (co)inductive theorem proving. While traditional proof system suffers some defects, non-wellfounded (or infinitary) and circular proofs have been recognized as a valuable alternative, and significant progress have been made in this direction in recent years. Such proofs are non-wellfounded sequent derivations together with a global validity condition expressed in terms of progressing threads. The present paper investigates a discrepancy found in such proof systems , between the sequential nature of sequent proofs and the parallel structure of threads: various proof attempts may have the exact threading structure while differing in the order of inference rules applications. The paper introduces infinets, that are proof-nets for non-wellfounded proofs in the setting of multiplicative linear logic with least and greatest fixed-points (µMLL ∞) and study their correctness and sequentialization

Infinets: The parallel syntax for non-wellfounded proof-theory

Logics based on the µ-calculus are used to model induc-tive and coinductive reasoning and to verify reactive systems. A well-structured proof-theory is needed in order to apply such logics to the study of programming languages with (co)inductive data types and automated (co)inductive theorem proving. While traditional proof system suffers some defects, non-wellfounded (or infinitary) and circular proofs have been recognized as a valuable alternative, and significant progress have been made in this direction in recent years. Such proofs are non-wellfounded sequent derivations together with a global validity condition expressed in terms of progressing threads. The present paper investigates a discrepancy found in such proof systems , between the sequential nature of sequent proofs and the parallel structure of threads: various proof attempts may have the exact threading structure while differing in the order of inference rules applications. The paper introduces infinets, that are proof-nets for non-wellfounded proofs in the setting of multiplicative linear logic with least and greatest fixed-points (µMLL ∞) and study their correctness and sequentialization. Inductive and coinductive reasoning is pervasive in computer science to specify and reason about infinite data as well as reactive properties. Developing appropriate proof systems amenable to automated reasoning over (co)inductive statements is therefore important for designing programs as well as for analyzing computational systems. Various logical settings have been introduced to reason about such inductive and coinductive statements, both at the level of the logical languages modelling (co)induction (such as Martin Löf's inductive predicates or fixed-point logics, also known as µ-calculi) and at the level of the proof-theoretical framework considered (finite proofs with explicit (co)induction rulesà la Park [23] or infinite, non-wellfounded proofs with fixed-point unfold-ings) [6-8, 4, 1, 2]. Moreover, such proof systems have been considered over classical logic [6, 8], intuitionistic logic [9], linear-time or branching-time temporal logic [19, 18, 25, 26, 13-15] or linear logic [24, 16, 4, 3, 14]

A situation risk awareness approach for process systems safety

Promoting situation awareness is an important design objective for a wide variety of domains, especially for process systems where the information flow is quite high and poor decisions may lead to serious consequences. In today's process systems, operators are often moved to a control room far away from the physical environment, and increasing amounts of information are passed to them via automated systems, they therefore need a greater level of support to control and maintain the facilities in safe conditions. This paper proposes a situation risk awareness approach for process systems safety where the effect of ever-increasing situational complexity on human decision-makers is a concern. To develop the approach, two important aspects - addressing hazards that arise from hardware failure and reducing human error through decision-making - have been considered. The proposed situation risk awareness approach includes two major elements: an evidence preparation component and a situation assessment component. The evidence preparation component provides the soft evidence, using a fuzzy partitioning method, that is used in the subsequent situation assessment component. The situation assessment component includes a situational network based on dynamic Bayesian networks to model the abnormal situations, and a fuzzy risk estimation method to generate the assessment result. A case from US Chemical Safety Board investigation reports has been used to illustrate the application of the proposed approach. © 2013 Elsevier Ltd

Demystifying μ\mu

We develop the theory of illfounded and cyclic proof systems in the context of the modal $\mu$-calculus. A fine analysis of provability and admissibility bridges the finitary, cyclic and illfounded notions of proof for this logic and re-enforces the subtlety of two important normal form theorems: guardedness and disjunctiveness

Improved False Causal Loop Detection in Polychronous Specificationof Embedded Software

As opposed to single clocked synchronous programming paradigms, polychronous formalism allows specification of concurrent data flow computation on signals such that various data flows can evolve asynchronous with respect to each other. Explicit constraints and constraints implied by the syntactic structures impart certain intrinsic properties to models specified polychronously. One of the major steps in designing a synthesis engine for polychronous specifications is the characterization of specified models into categories such as inherently sequential or inherently multi-threaded. In this paper, we are concerned with sequentially implementable polychronous specification where computation is divided into a totally ordered sequence of logical instants. Data flow computation within an instant happens based on the implied data flow order. This order or data dependency often varies from one instant to another. Thus determining if there is an instant at which the data flow order forms a causal cycle is an important problem. In the current polychronous compilers, such as SIGNAL compiler and EmCodeSyn, this is solved without due effort, by rejecting any program which has a buffer-free structural cycle. However, a clocked dependency graph can be used to construct logical constraints representing the instants with a possible causal loop. The satisfiability of such constraints would imply that such a loop is realizable and hence the specification has a possible deadlock. The reachability of this instant with a given set of initial conditions would verify if the program should be rejected. In the past, the work on such constraints and their satisfiability has not been implemented even though for pure Boolean signals and clocks this could have been done using a satisfiability solver. With the advent to SAT modulo theory (SMT) solvers, this can now be extended to a more general class of specifications. Moreover, model checking on an abstraction of the specification can provide more information about the reachability of instants at which cyclic data dependency is realized. This paper presents an improved polychronous synthesis tool accepting a much larger class of specifications than could be done before. In our experimental results, we demonstrate the capabilities of our causality analysis methods and show that our synthesis tool performs better than previous strategies, including our own past work