The Grail theorem prover: Type theory for syntax and semantics

As the name suggests, type-logical grammars are a grammar formalism based on logic and type theory. From the prespective of grammar design, type-logical grammars develop the syntactic and semantic aspects of linguistic phenomena hand-in-hand, letting the desired semantics of an expression inform the syntactic type and vice versa. Prototypical examples of the successful application of type-logical grammars to the syntax-semantics interface include coordination, quantifier scope and extraction.This chapter describes the Grail theorem prover, a series of tools for designing and testing grammars in various modern type-logical grammars which functions as a tool . All tools described in this chapter are freely available

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

Hybrid performance modelling of opportunistic networks

We demonstrate the modelling of opportunistic networks using the process algebra stochastic HYPE. Network traffic is modelled as continuous flows, contact between nodes in the network is modelled stochastically, and instantaneous decisions are modelled as discrete events. Our model describes a network of stationary video sensors with a mobile ferry which collects data from the sensors and delivers it to the base station. We consider different mobility models and different buffer sizes for the ferries. This case study illustrates the flexibility and expressive power of stochastic HYPE. We also discuss the software that enables us to describe stochastic HYPE models and simulate them.Comment: In Proceedings QAPL 2012, arXiv:1207.055

On Computational Small Steps and Big Steps: Refocusing for Outermost Reduction

We study the relationship between small-step semantics, big-step semantics and abstract machines, for programming languages that employ an outermost reduction strategy, i.e., languages where reductions near the root of the abstract syntax tree are performed before reductions near the leaves.In particular, we investigate how Biernacka and Danvy's syntactic correspondence and Reynolds's functional correspondence can be applied to inter-derive semantic specifications for such languages.The main contribution of this dissertation is three-fold:First, we identify that backward overlapping reduction rules in the small-step semantics cause the refocusing step of the syntactic correspondence to be inapplicable.Second, we propose two solutions to overcome this in-applicability: backtracking and rule generalization.Third, we show how these solutions affect the other transformations of the two correspondences.Other contributions include the application of the syntactic and functional correspondences to Boolean normalization.In particular, we show how to systematically derive a spectrum of normalization functions for negational and conjunctive normalization

Towards a bigraphical encoding of actors

Actors are self-contained, concurrently interacting entities of a computing system. They can perform local computations, communicate via asynchronous message passing with other actors and can be dynamically created. Bigraphs are a fully graphical process algebraic formalism, capable of representing both the position in space of agents and their inter-connections. Their behaviour is specified by a set of reaction rules. In this paper, we present a bigraphical encoding of a simplified actor language with static topology. We express actor configurations in terms of sorted bigraphs while the rules of the actor operational semantics are encoded by bigraphical reactive rules

Topological Calculus of Looping Sequences

Il Calculus of Looping Sequences (CLS) permette la descrizione dei sistemi biologici e della loro evoluzione. Nell'ambito del lavoro di tesi e' stata sviluppata una estensione del CLS, chiamata Topological CLS (TCLS), dove ad ogni oggetto del sistema biologico sono associate una precisa posizione e dimensione nello spazio. Gli oggetti possono muoversi autonomamente e l'applicabilita' delle regole di riscrittura, che modellano le reazioni tra gli elementi, puo' essere determinata dalle posizioni degli oggetti coinvolti. Infine, alle regole di riscrittura e' associato un parametro che ne specifica la velocita' di reazione. Il Topological CLS e' stato quindi utilizzato per modellare due esempi di sistemi biologici: il processo di mitosi e il quorum-sensing