Related papers: Multi-Sequential Word Relations
Default logic encounters some conceptual difficulties in representing common sense reasoning tasks. We argue that we should not try to formulate modular default rules that are presumed to work in all or most circumstances. We need to take…
The functional approach to compositional distributional semantics considers transitive verbs to be linear maps that transform the distributional vectors representing nouns into a vector representing a sentence. We conduct an initial…
Refinement calculus is a powerful and expressive tool for reasoning about sequential programs in a compositional manner. In this paper we present an extension of refinement calculus for reactive systems. Refinement calculus is based on…
Set functions are a feature of functional logic programming to encapsulate all results of a non-deterministic computation in a single data structure. Given a function $f$ of a functional logic program written in Curry, we describe a…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
Analyzing relational languages by their logical expressiveness is well understood. Something not well understood or even formalized is the vague concept of relational query patterns. What are query patterns? And how can we reason about…
In this paper, we show that, under mild assumptions, input-output behavior of a continous-time recurrent neural network (RNN) can be represented by a rational or polynomial nonlinear system. The assumptions concern the activation function…
We revisit the membership problem for subclasses of rational relations over finite and infinite words: Given a relation R in a class C_2, does R belong to a smaller class C_1? The subclasses of rational relations that we consider are formed…
Sequential modelling entails making sense of sequential data, which naturally occurs in a wide array of domains. One example is systems that interact with users, log user actions and behaviour, and make recommendations of items of potential…
A definition for functions of multidimensional arrays is presented. The definition is valid for third-order tensors in the tensor t-product formalism, which regards third-order tensors as block circulant matrices. The tensor function…
Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
Let k be an algebraically closed field of characteristic zero. An element F from k(x_1,...,x_n) is called a closed rational function if the subfield k(F) is algebraically closed in the field k(x_1,...,x_n). We prove that a rational function…
In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data omega-words). The notion of computability is defined through Turing machines with infinite inputs which can…
The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$…
In this paper, we study the continuity of rational functions realized by B\"uchi finite state transducers. It has been shown by Prieur that it can be decided whether such a function is continuous. We prove here that surprisingly, it cannot…
Discourse relations bind smaller linguistic units into coherent texts. However, automatically identifying discourse relations is difficult, because it requires understanding the semantics of the linked arguments. A more subtle challenge is…
In decentralized stochastic control (or stochastic team theory) and game theory, if there is a pre-defined order in a system in which agents act, the system is called \textit{sequential}, otherwise it is non-sequential. Much of the…
The identification of semantic relations between terms within texts is a fundamental task in Natural Language Processing which can support applications requiring a lightweight semantic interpretation model. Currently, semantic relation…
We consider the synthesis of deterministic tree transducers from automaton definable specifications, given as binary relations, over finite trees. We consider the case of specifications that are deterministic top-down tree automatic,…