Related papers: A Case Study on Logical Relations using Contextual…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…
We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…
In any setting in which observable properties have a quantitative flavour, it is natural to compare computational objects by way of \emph{metrics} rather than equivalences or partial orders. This holds, in particular, for probabilistic…
Applying machine learning algorithms to large-scale, text-based corpora (embeddings) presents a unique opportunity to investigate at scale how human semantic knowledge is organized and how people use it to judge fundamental relationships,…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
We present a proof-theoretic analysis of the logic NL$\lambda$ (Barker \& Shan 2014, Barker 2019). We notably introduce a novel calculus of proof nets and prove it is sound and complete with respect to the sequent calculus for the logic. We…
The connection between normalization by evaluation, logical predicates and semantic gluing constructions is a matter of folklore, worked out in varying degrees within the literature. In this note, we present an elementary version of the…
Incorporating external knowledge is crucial for knowledge-intensive tasks, such as question answering and fact checking. However, language models (LMs) may ignore relevant information that contradicts outdated parametric memory or be…
Dependently typed lambda calculi such as the Edinburgh Logical Framework (LF) are a popular means for encoding rule-based specifications concerning formal syntactic objects. In these frameworks, relations over terms representing formal…
A recent framework of relativized hyperequivalence of programs offers a unifying generalization of strong and uniform equivalence. It seems to be especially well suited for applications in program optimization and modular programming due to…
Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…
We give a simple, direct and reusable logical relations technique for languages with term and type recursion and partially defined differentiable functions. We demonstrate it by working out the case of Automatic Differentiation (AD)…
In recent years, large pretrained models have been used in dialogue systems to improve successful task completion rates. However, lack of reasoning capabilities of dialogue platforms make it difficult to provide relevant and fluent…
The logico-pluralist LogiKEy knowledge engineering methodology and framework is applied to the modelling of a theory of legal balancing in which legal knowledge (cases and laws) is encoded by utilising context-dependent value preferences.…
The vital role of analogical reasoning in human cognition allows us to grasp novel concepts by linking them with familiar ones through shared relational structures. Despite the attention previous research has given to word analogies, this…
The $\lambda$-calculus is a handy formalism to specify the evaluation of higher-order programs. It is not very handy, however, when one interprets the specification as an execution mechanism, because terms can grow exponentially with the…
The ease and speed of spreading misinformation and propaganda on the Web motivate the need to develop trustworthy technology for detecting fallacies in natural language arguments. However, state-of-the-art language modeling methods exhibit…
Recent research demonstrates the effectiveness of using pre-trained language models for legal case retrieval. Most of the existing works focus on improving the representation ability for the contextualized embedding of the [CLS] token and…