A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time

Interval Temporal Logic (ITL) is an established temporal formalism for reasoning about time periods. For over 25 years, it has been applied in a number of ways and several ITL variants, axiom systems and tools have been investigated. We solve the longstanding open problem of finding a complete axiom system for basic quantifier-free propositional ITL (PITL) with infinite time for analysing nonterminating computational systems. Our completeness proof uses a reduction to completeness for PITL with finite time and conventional propositional linear-time temporal logic. Unlike completeness proofs of equally expressive logics with nonelementary computational complexity, our semantic approach does not use tableaux, subformula closures or explicit deductions involving encodings of omega automata and nontrivial techniques for complementing them. We believe that our result also provides evidence of the naturalness of interval-based reasoning

Computing Branching Distances Using Quantitative Games

We lay out a general method for computing branching distances between labeled transition systems. We translate the quantitative games used for defining these distances to other, path-building games which are amenable to methods from the theory of quantitative games. We then show for all common types of branching distances how the resulting path-building games can be solved. In the end, we achieve a method which can be used to compute all branching distances in the linear-time--branching-time spectrum

Extensible Proof Systems for Infinite-State Systems

This article revisits soundness and completeness of proof systems for proving that sets of states in infinite-state labeled transition systems satisfy formulas in the modal mu-calculus in order to develop proof techniques that permit the seamless inclusion of new features in this logic. Our approach relies on novel results in lattice theory, which give constructive characterizations of both greatest and least fixpoints of monotonic functions over complete lattices. We show how these results may be used to reason about the sound and complete tableau method for this problem due to Bradfield and Stirling. We also show how the flexibility of our lattice-theoretic basis simplifies reasoning about tableau-based proof strategies for alternative classes of systems. In particular, we extend the modal mu-calculus with timed modalities, and prove that the resulting tableau method is sound and complete for timed transition systems

LFTOP: An LF based approach to domain specific reasoning

Specialized vocabulary, notations and inference rules tailored for the description, analysis and reasoning of a domain is very important for the domain. For domain-specific issues researchers focus mainly on the design and implementation of domain-specific languages (DSL) and pay little attention to the reasoning aspects. We believe that domain-specific reasoning is very important to help the proofs of some properties of the domains and should be more concise, more reusable and more believable. It deserves to be investigated in an engineering way. Type theory provides good support for generic reasoning and verification. Many type theorists want to extend uses of type theory to more domains, and believe that the methods, ideas, and technology of type theory can have a beneficial effect for computer assisted reasoning in many domains. Proof assistants based on type theory are well known as effective tools to support reasoning. But these proof assistants have focused primarily on generic notations for representation of problems and are oriented towards helping expert type theorists build proofs efficiently. They are successful in this goal, but they are less suitable for use by non-specialists. In other words, one of the big barriers to limit the use of type theory and proof assistant in domain-specific areas is that it requires significant expertise to use it effectively. We present LFTOP ― a new approach to domain-specific reasoning that is based on a type-theoretic logical framework (LP) but does not require the user to be an expert in type theory. In this approach, users work on a domain-specific interface that is familiar to them. The interface presents a reasoning system of the domain through a user-oriented syntax. A middle layer provides translation between the user syntax and LF， and allows additional support for reasoning (e.g. model checking). Thus, the complexity of the logical framework is hidden but we also retain the benefits of using type theory and its related tools, such as precision and machine-checkable proofs. The approach is being investigated through a number of case studies. In each case study, the relevant domain-specific specification languages and logic are formalized in Plastic. The relevant reasoning system is designed and customized for the users of the corresponding specific domain. The corresponding lemmas are proved in Plastic. We analyze the advantages and shortcomings of this approach, define some new concepts related to the approach, especially discuss issues arising from the translation between the different levels. A prototype implementation is developed. We illustrate the approach through many concrete examples in the prototype implementation. The study of this thesis shows that the approach is feasible and promising, the relevant methods and technologies are useful and effective

Homotopy Bisimilarity for Higher-Dimensional Automata

We introduce a new category of higher-dimensional automata in which the morphisms are functional homotopy simulations, i.e. functional simulations up to concurrency of independent events. For this, we use unfoldings of higher-dimensional automata into higher-dimensional trees. Using a notion of open maps in this category, we define homotopy bisimilarity. We show that homotopy bisimilarity is equivalent to a straight-forward generalization of standard bisimilarity to higher dimensions, and that it is finer than split bisimilarity and incomparable with history-preserving bisimilarity.Comment: Heavily revised version of arXiv:1209.492

A Computational Framework of Human Values

There is an increasing recognition of the need to engineer AI that respects and embodies human values. The value alignment problem, which identifies that need, has led to a growing body of research that investigates value learning, the aggregation of individual values into the values of groups, the alignment of norms with values, and the design of other computational mechanisms that reason over values in general. Yet despite these efforts, no foundational, computational model of human values has been proposed. In response, we propose a model for the computational representation of human values that builds upon a sustained body of research from social psychology

Symbolic planning for heterogeneous robots through composition of their motion description languages

This dissertation introduces a new formalism to define compositions of interacting heterogeneous systems, described by extended motion description languages (MDLes). The properties of the composition system are analyzed and an automatic process to generate sequential atom plan is introduced. The novelty of the formalism is in producing a composed system with a behavior that could be a superset of the union of the behaviors of its generators. As robotic systems perform increasingly complex tasks, people resort increasingly to switching or hybrid control algorithms. A need arises for a formalism to compose different robotic behaviors and meet a final target. The significant work produced to date on various aspects of robotics arguably has not yet effectively captured the interaction between systems. Another problem in motion control is automating the process of planning and it has been recognized that there is a gap between high level planning algorithms and low level motion control implementation. This dissertation is an attempt to address these problems. A new composition system is given and the properties are checked. We allow systems to have additional cooperative transitions and become active only when the systems are composed with other systems appropriately. We distinguish between events associated with transitions a push-down automaton representing an MDLe can take autonomously, and events that cannot initiate transitions. Among the latter, there can be events that when synchronized with some of another push-down automaton, become active and do initiate transitions. We identify MDLes as recursive systems in some basic process algebra (BPA) written in Greibach Normal Form. By identifying MDLes as a subclass of BPAs, we are able to borrow the syntax and semantics of the BPAs merge operator (instead of defining a new MDLe operator), and thus establish closeness and decidability properties for MDLe compositions. We introduce an instance of the sliding block puzzle as a multi-robot hybrid system. We automate the process of planning and dictate how the behaviors are sequentially synthesized into plans that drive the system into a desired state. The decidability result gives us hope to abstract the system to the point that some of the available model checkers can be used to construct motion plans. The new notion of system composition allows us to capture the interaction between systems and we realize that the whole system can do more than the sum of its parts. The framework can be used on groups of heterogeneous robotic systems to communicate and allocate tasks among themselves, and sort through possible solutions to find a plan of action without human intervention or guidance

Congruent Weak Conformance

This research addresses the problem of verifying implementations against specifications through an innovative logic approach. Congruent weak conformance, a formal relationship between agents and specifications, has been developed and proven to be a congruent partial order. This property arises from a set of relations called weak conformations. The largest, called weak conformance, is analogous to Milner\u27s observational equivalence. Weak conformance is not an equivalence, however, but rather an ordering relation among processes. Weak conformance allows behaviors in the implementation that are unreachable in the specification. Furthermore, it exploits output concurrencies and allows interleaving of extraneous output actions in the implementation. Finally, reasonable restrictions in CCS syntax strengthen weak conformance to a congruence, called congruent weak conformance. At present, congruent weak conformance is the best known formal relation for verifying implementations against specifications. This precongruence derives maximal flexibility and embodies all weaknesses in input, output, and no-connect signals while retaining a fully replaceable conformance to the specification. Congruent weak conformance has additional utility in verifying transformations between systems of incompatible semantics. This dissertation describes a hypothetical translator from the informal simulation semantics of VHDL to the bisimulation semantics of CCS. A second translator is described from VHDL to a broadcast-communication version of CCS. By showing that they preserve congruent weak conformance, both translators are verified