Related papers: Towards Nominal Formal Languages
We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…
We construct a formal theory, which we call reflectica, whose language possesses the following properties of natural language: it is a self-reflecting language and an intensional language. By a self-reflecting language we understand an…
We investigate the formal semantics of a simple imperative language that has both classical and quantum constructs. More specifically, we provide an operational semantics, a denotational semantics and two Hoare-style proof systems: an…
Symbolic automata are finite state automata that support potentially infinite alphabets, such as the set of rational numbers, generally applied to regular expressions/languages over finite words. In symbolic automata (or automata modulo…
A novel formalisation of variable control in languages with implicit names based on de Bruijn indices is presented. We design and implement three languages: first, a restricted language with implicit names; then, a restricted calculus with…
Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
Formal languages over infinite alphabets serve as abstractions of structures and processes carrying data. Automata models over infinite alphabets, such as classical register automata or, equivalently, nominal orbit-finite automata, tend to…
We introduce Nominal Matching Logic (NML) as an extension of Matching Logic with names and binding following the Gabbay-Pitts nominal approach. Matching logic is the foundation of the $\mathbb{K}$ framework, used to specify programming…
Nominalization is a highly productive phenomena in most languages. The process of nominalization ejects a verb from its syntactic role into a nominal position. The original verb is often replaced by a semantically emptied support verb…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category D. This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the syntactic monoids…
We consider forkable regular expressions, which enrich regular expressions with a fork operator, to establish a formal basis for static and dynamic analysis of the communication behavior of concurrent programs. We define a novel…
In this paper we regard languages and their acceptors -- such as deterministic or weighted automata, transducers, or monoids -- as functors from input categories that specify the type of the languages and of the machines to categories that…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…
Using recent developments in coalgebraic and monad-based semantics, we present a uniform study of various notions of machines, e.g. finite state machines, multi-stack machines, Turing machines, valence automata, and weighted automata. They…
The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful…
We develop an algebraic language theory based on the notion of an Eilenberg--Moore algebra. In comparison to previous such frameworks the main contribution is the support for algebras with infinitely many sorts and the connection to logic…
A bialgebra is a structure which is simultaneously an algebra and a coalgebra, such that the algebraic and coalgebraic parts are "compatible". Bialgebras are normally studied over a field or commutative ring. In this paper, we show how to…