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Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
We study the complexity of reasoning tasks for logics in team semantics. Our main focus is on the data complexity of model checking but we also derive new results for logically defined counting and enumeration problems. Our approach is…
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…
As an attempt to uncover the topological nature of composition of strategies in game semantics, we present a ``topological'' game for Multiplicative Additive Linear Logic without propositional variables, including cut moves. We recast the…
Differential categories were introduced to provide a minimal categorical doctrine for differential linear logic. Here we revisit the formalism and, in particular, examine the two different approaches to defining differentiation which were…
We show that if we enrich first order logic by allowing quantification over isomorphisms between definable ordered fields the resulting logic, L(Q_{Of}), is fully compact. In this logic, we can give standard compactness proofs of various…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
We provide a new realisability model based on orthogonality for the multiplicative fragment of linear logic, both in presence of generalised axioms (MLL*) and in the standard case (MLL). The novelty is the definition of cut elimination for…
Learning policies that effectively utilize language instructions in complex, multi-task environments is an important problem in sequential decision-making. While it is possible to condition on the entire language instruction directly, such…
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…
Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more…
Designing effective and efficient classifier for pattern analysis is a key problem in machine learning and computer vision. Many the solutions to the problem require to perform logic operations such as `and', `or', and `not'. Classification…
In this paper, we consider a simple class of stratified spaces -- 2-complexes. We present an algorithm that learns the abstract structure of an embedded 2-complex from a point cloud sampled from it. We use tools and inspiration from…
Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…
Abstract algebraic logic is a theory that provides general tools for the algebraic study of arbitrary propositional logics. According to this theory, every logic L is associated with a matrix semantics Mod*(L). This paper is a contribution…
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…