On the generative capacity of multi-modal Categorial Grammars

In Moortgat 1996 the Lambek Calculus L (Lambek 1958) is extended by a pair of residuation modalities ◊ and □↓. Categorial Grammars based on the resulting logic L◊ are attractive for linguistic purposes since they offer a compromise between the strict constituent structures imposed by context free grammars and related formalisms on the one hand, and the complete absence of hierarchical information in Lambek grammars on the other hand. The paper contains some results on the generative capcity of Categorial Grammars based on L◊. First it is shown that adding residuation modalities does not extend the weak generative capacity. This is proved by extending the proof for the context freeness of L-grammars from Pentus 1993 to L◊. Second the strong generative capacity of L◊-grammars is compared to context free grammars. The results are mainly negative. The set of tree languages generated by L◊-grammars neither contains nor is contained in the class of context free tree languages

A Constraint-based Language for Multiparty Interactions.

Abstract Multiparty interactions are common place in today's distributed systems. An agent usually communicates, in a single session, with other agents to accomplish a given task. Take for instance an online transaction including the vendor, the client, the credit card system and the bank. When specifying this kind of system, we probably observe a single transaction including several (binary) communications leading to changes in the state of all the involved agents. Multiway synchronization process calculi, that move from a binary to a multiparty synchronization discipline, have been proposed to formally study the behavior of those systems. However, adopting models such as Bodei, Brodo, and Bruni's Core Network Algebra (CNA), where the number of participants in an interaction is not fixed a priori, leads to an exponential blow-up in the number of states/behaviors that can be observed from the system. In this paper we explore mechanisms to tackle this problem. We extend CNA with constraints that declaratively allow the modeler to restrict the interaction that should actually happen. Our extended process algebra, called CCNA, finds application in balancing the interactions in a concurrent system, leading to a simple, deadlock-free and fair solution for the Dinning Philosopher problem. Our definition of constraints is general enough and it offers the possibility of accumulating costs in a multiparty negotiation. Hence, only computations respecting the thresholds imposed by the modeler are observed. We use this machinery to neatly model a Service Level Agreement protocol. We develop the theory of CCNA including its operational semantics and a behavioral equivalence that we prove to be a congruence. We also propose a prototypical implementation that allows us to verify, automatically, some of the systems explored in the paper

Full Nonassociative Lambek Calculus with Modalities and Its Applications in Type Grammars

Wydział Matematyki i InformatykiRozprawa jest poświęcona pełnemu niełącznemu rachunkowi Lambeka wzbogaconemu o różne modalności. Te systemy tworzą pewną rodzinę logik substrukturalnych. W rozprawie badamy rachunki NL (niełączny rachunek Lambeka), DFNL (pełny niełączny rachunek Lambeka z prawami dystrybutywności dla operacji kratowych) i BFNL (DFNL z negacją spełniającą prawa algebr Boole’a) oraz ich rozszerzenia o operatory modalne, tworzące parę rezyduacji i spełniające standardowe aksjomaty logik modalnych (T), (4) i (5). Rozważamy też gramatyki typów oparte na tych rachunkach. Główne wyniki: twierdzenie o eliminacji cięć dla modalnych rozszerzeń NL z założeniami, wielomianowa złożoność relacji konsekwencji dla tych systemów, lemat interpolacyjny dla modalnych rozszerzeń DFNL i BFNL z założeniami, silna własność skończonego modelu dla tych systemów, rozstrzygalność relacji konsekwencji dla tyc systemów, PSPACE-zupełność rachunku BFNL, bezkontekstowość języków generowanych przez gramatyki typów oparte na tych rachunkach. Rozprawa kontynuuje wcześniejsze badania W. Buszkowskiego, M. Farulewskiego, M. Moortgata, A.. Plummera, N. Kurtoniny i innych.The thesis is devoted to full nonassociative Lambek calculus enriched with different modalities. These systems form a family of substrutural logics. In this thesis we study systems NL (nonassociative Lambek calculus), DFNL (full nonassociative Lambek calculus with the distributive laws for lattice operations) and BFNL (DFNL with negation satisfying the laws of Boolean algebras) and their extensions by modal operators, being a residuation pair and fulfilling standard axioms of modal logics (T), (4), (5). We also consider the type grammars based on these calculi. Main results: the cut-elimination theorem for modal extensions of NL with assumptions, the polynomial-time complexity of the consequence relations for these systems, an interpolation lemma for modal extensions of DFNL and BFNL with assumptions, the strong finite model property of the latter systems, the decidability of the consequence relations for the latter systems, the PSPACE-completeness of BFNL, the context-freeness of the languages generated by the type grammars based on these systems. The thesis continues some research of W. Buszkowski, M. Farulewski, M. Moortgat, A. Plummer,, N. Kurtonina and others

Dynamic Awareness

This paper proposes, firstly, a versatile model of awareness and awareness change, and secondly, logics for awareness and awareness change developed using this model.Awareness; knowledge; logic of awareness; awareness change; belief revision.

Meaning versus Grammar

This volume investigates the complicated relationship between grammar, computation, and meaning in natural languages. It details conditions under which meaning-driven processing of natural language is feasible, discusses an operational and accessible implementation of the grammatical cycle for Dutch, and offers analyses of a number of further conjectures about constituency and entailment in natural language

Using pattern-action rules for the generation of GPSG structures from separate semantic representations

In many tactical NL generators the semantic input structure is taken for granted. In this paper, a new approach to multilingual, tactical generation is presented that keeps the syntax separate from the semantics. This allows for the system to be directly adapted to application-dependent representations. In the case at hand, the semantics is specifically designed for sentence-semantic transfer in a machine translation system. The syntax formalism used is Generalized Phrase Structure Grammar (GPSG). The mapping from semantic onto syntactic structures is performed by a set of pattern-action rules. Each rule matches a piece of the input structure and guides the GPSG structure-building process by telling it which syntax rule(s) to apply. The scope of each pattern-action rule is strictly local, the actions are primitive, and rules can not call each other. These restrictions render the production rule approach both highly modular and transparent