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State-of-the-art visual grounding models can achieve high detection accuracy, but they are not designed to distinguish between all objects versus only certain objects of interest. In natural language, in order to specify a particular object…
It is well known that dependence logic captures the complexity class NP, and it has recently been shown that inclusion logic captures P on ordered models. These results demonstrate that team semantics offers interesting new possibilities…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
Diffractive optical neural networks (DONNs) have attracted lots of attention as they bring significant advantages in terms of power efficiency, parallelism, and computational speed compared with conventional deep neural networks (DNNs),…
The paper is devoted to showing how to systematically design a programming language in 'reverse order', i.e. from denotations to syntax. This construction is developed in an algebraic framework consisting of three many-sorted algebras: of…
Many formal languages include binders as well as operators that satisfy equational axioms, such as commutativity. Here we consider the nominal language, a general formal framework which provides support for the representation of binders,…
We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
The recently introduced dependent typed higher-order logic (DHOL) offers an interesting compromise between expressiveness and automation support. It sacrifices the decidability of its type system in order to significantly extend its…
NOOP is a mathematical model of nominally-typed OOP that proves the identification of inheritance and subtyping in mainstream nominally-typed OO programming languages and the validity of this identification. This report gives an overview of…
This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic…
Configurable systems typically consist of reusable assets that have dependencies between each other. To specify such dependencies, feature models are commonly used. As feature models in practice are often complex, automated reasoning is…
We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which…
Dependently typed proof assistant rely crucially on definitional equality, which relates types and terms that are automatically identified in the underlying type theory. This paper extends type theory with definitional functor laws,…
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…
This dissertation introduces executable refinement types, which refine structural types by semi-decidable predicates, and establishes their metatheory and accompanying implementation techniques. These results are useful for undecidable type…
Deverbal nouns are nominal forms of verbs commonly used in written English texts to describe events or actions, as well as their arguments. However, many NLP systems, and in particular pattern-based ones, neglect to handle such nominalized…
This paper proposes a modal typing system that enables us to handle self-referential formulae, including ones with negative self-references, which on one hand, would introduce a logical contradiction, namely Russell's paradox, in the…
We present a novel approach to construction of a formal semantics for a programming language. Our approach, using a parametric denotational semantics, allows the semantics to be easily extended to support new language features, and…
A desired but challenging property of compiler verification is compositionality, in the sense that the compilation correctness of a program can be deduced incrementally from that of its substructures ranging from statements, functions, and…