Related papers: Shift spaces, Languages and Transfinite Induction
Polysemy and synonymy are two crucial interrelated facets of lexical ambiguity. While both phenomena are widely documented in lexical resources and have been studied extensively in NLP, leading to dedicated systems, they are often being…
Internal preneighbourhood spaces inside any finitely complete category with finite coproducts and proper factorisation structure were first introduced in my earlier paper. This paper proposes a closure operation on internal preneighbourhood…
A subunit in a monoidal category is a subobject of the monoidal unit for which a canonical morphism is invertible. They correspond to open subsets of a base topological space in categories such as those of sheaves or Hilbert modules. We…
We introduce a simple property, affine invariance, which characterizes within the class of fuzzy topological spaces those which are induced from an underlying topology on the space. We illustrate it by considering the simple notions of…
The shift locus is the space of normalized polynomials in one complex variable for which every critical point is in the attracting basin of infinity. The method of sausages gives a (canonical) decomposition of the shift locus in each degree…
This note explains how dependent sums and products are interpreted by adjoints of the base change functor in a locally cartesian closed category. An effort is made to unpack all the definitions so as to make the concepts more transparent to…
Transfer learning is a vital technique that generalizes models trained for one setting or task to other settings or tasks. For example in speech recognition, an acoustic model trained for one language can be used to recognize speech in…
The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
This paper initiates the dialectical approach to net theory. This approach views nets as special, but very important and natural, dialectical systems. By following this approach, a suitably generalized version of nets, called dialectical…
The synthesis of string transformation programs from input-output examples utilizes various techniques, all based on an inductive bias that comprises a restricted set of basic operators to be combined. A new algorithm, Transduce, is…
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…
Shuffle projection is motivated by the verification of safety properties of special parameterized systems. Basic definitions and properties, especially related to alphabetic homomorphisms, are presented. The relation between iterated…
We consider reflexive and involutive transition systems over an ordered alphabet $A$ equipped with an involution. We give a description of the injective envelope of any two-element set in terms of Galois lattice, from which we derive a test…
In a polar space, embeddable into a projective space, we fix a subspace, that is contained in some hyperplane. The complement of that subspace resembles a slit space or a semiaffine space. We prove that under some assumptions the ambient…
This paper extends implication-space semantics to include first-order quantification. Implication-space semantics has recently been introduced as an inferentialist formal semantics that can capture nonmonotonic and nontransitive material…
Several variations on the definition of a Formal Topology exist in the literature. They differ on how they express convergence, the formal property corresponding to the fact that open subsets are closed under finite intersections. We…
A subshift of finite type over finitely many symbols can be described as a collection of all infinite walks on a digraph with at most a single edge from a vertex to another. The associated finite set $\F$ of forbidden words is a constraint…
Latent space is rapidly emerging as a native substrate for language-based models. While modern systems are still commonly understood through explicit token-level generation, an increasing body of work shows that many critical internal…
This paper investigates an unsupervised approach towards deriving a universal, cross-lingual word embedding space, where words with similar semantics from different languages are close to one another. Previous adversarial approaches have…