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We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
We present a symbolic transition system and bisimulation equivalence for psi-calculi, and show that it is fully abstract with respect to bisimulation congruence in the non-symbolic semantics. A psi-calculus is an extension of the…
We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a parallel and more powerful extension of the simply typed lambda calculus corresponding to an analytic natural deduction based on the excluded…
Recently, Logic Explained Networks (LENs) have been proposed as explainable-by-design neural models providing logic explanations for their predictions. However, these models have only been applied to vision and tabular data, and they mostly…
Aligning language models (LMs) with user intent is becoming increasingly relevant to enhance user experience. This calls for designing methods that can allow users to control the properties of the language that LMs generate, for example,…
Semantic parsing is a means of taking natural language and putting it in a form that a computer can understand. There has been a multitude of approaches that take natural language utterances and form them into lambda calculus expressions --…
We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than…
The pi-calculus is a widely used process calculus, which models communications between processes and allows the passing of communication links. Various operational semantics of the pi-calculus have been proposed, which can be classified…
We present a C-language implementation of the lambda-pi calculus by extending the (call-by-need) stack machine of Ariola, Chang and Felleisen to hold types, using a typeless- tagless- final interpreter strategy. It has the advantage of…
Psi-calculi is a parametric framework for extensions of the pi-calculus with data terms and arbitrary logics. In this framework there is no direct way to represent action priorities, where an action can execute only if all other enabled…
This paper addresses the problem of mapping natural language sentences to lambda-calculus encodings of their meaning. We describe a learning algorithm that takes as input a training set of sentences labeled with expressions in the lambda…
We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both…
It is important to enable reasoning about the meaning and possible effects of updates to ensure that the updated system operates correctly. A formal, mathematical model of dynamic update should be developed, in order to understand by both…
Relative monads provide a controlled view of computation. We generalise the monadic metalanguage to a relative setting and give a complete semantics with strong relative monads. Adopting this perspective, we generalise two existing program…
In this paper we examine the limitations of Large Language Models (LLMs) for complex reasoning tasks. Although recent works have started to employ formal languages as an intermediate representation for reasoning tasks, they often face…
While pre-trained language models (LMs) have brought great improvements in many NLP tasks, there is increasing attention to explore capabilities of LMs and interpret their predictions. However, existing works usually focus only on a certain…
Despite emerging research on Language Models (LM), few approaches analyse the invertibility of LMs. That is, given a LM and a desirable target output sequence of tokens, determining what input prompts would yield the target output remains…
Semantics of a sentence is defined with much less ambiguity than semantics of a single word, and we assume that it should be better preserved by translation to another language. If multilingual sentence embeddings intend to represent…
Neural language models (LMs) represent facts about the world described by text. Sometimes these facts derive from training data (in most LMs, a representation of the word "banana" encodes the fact that bananas are fruits). Sometimes facts…
Recently, large language models (LLMs) have shown remarkable capabilities including understanding context, engaging in logical reasoning, and generating responses. However, this is achieved at the expense of stringent computational and…