Related papers: Congruence from the Operator's Point of View: Comp…
We show that three fixed point structures equipped with (sequential) composition, a sum operation, and a fixed point operation share the same valid equations. These are the theories of (context-free) languages, (regular) tree languages, and…
Compositional learning, mastering the ability to combine basic concepts and construct more intricate ones, is crucial for human cognition, especially in human language comprehension and visual perception. This notion is tightly connected to…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
In standard process algebra, parallel components do not share a common state and communicate through synchronisation. The advantage of this type of communication is that it facilitates compositional reasoning. For modelling and analysing…
We investigate two specific manifestations of compositionality in Neural Machine Translation (NMT) : (1) Productivity - the ability of the model to extend its predictions beyond the observed length in training data and (2) Systematicity -…
Semantic compositionality (SC) refers to the phenomenon that the meaning of a complex linguistic unit can be composed of the meanings of its constituents. Most related works focus on using complicated compositionality functions to model SC…
This paper contributes to the mathematical foundations of logic programming by introducing and studying the sequential composition of answer set programs. On the semantic side, we show that the immediate consequence operator of a program…
We consider systems of rational agents who act and interact in pursuit of their individual and collective objectives. We study and formalise the reasoning of an agent, or of an external observer, about the expected choices of action of the…
This work proposes a novel methodology for measuring compositional behavior in contemporary language embedding models. Specifically, we focus on adjectival modifier phenomena in adjective-noun phrases. In recent years, distributional…
We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
Orthogonality is a discipline of programming that in a syntactic manner guarantees determinism of functional specifications. Essentially, orthogonality avoids, on the one side, the inherent ambiguity of non determinism, prohibiting the…
In this paper I distinguish two (pre)congruence requirements for semantic equivalences and preorders on processes given as closed terms in a system description language with a recursion construct. A lean congruence preserves equivalence…
Systematic compositionality is the ability to recombine meaningful units with regular and predictable outcomes, and it's seen as key to humans' capacity for generalization in language. Recent work has studied systematic compositionality in…
Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
Previous results on proving confluence for Constraint Handling Rules are extended in two ways in order to allow a larger and more realistic class of CHR programs to be considered confluent. Firstly, we introduce the relaxed notion of…
Alignments, i.e., position-wise comparisons of two or more strings or ordered lists are of utmost practical importance in computational biology and a host of other fields, including historical linguistics and emerging areas of research in…
Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term…