Related papers: Relational semantics of linear logic and higher-or…
This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we…
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…
Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…
Model checking is an automatic formal verification technique that is widely used in hardware verification. The state-of-the-art complete model-checking techniques, based on IC3/PDR and its general variant CAR, are based on computing…
The quadratic cost of scaled dot-product attention is a central obstacle to scaling autoregressive language models to long contexts. Linear-time attention and State Space Models (SSMs) provide scalable alternatives but are typically…
There are two kinds of higher-order extensions of model checking: HORS model checking and HFL model checking. Whilst the former has been applied to automated verification of higher-order functional programs, applications of the latter have…
This paper develops a novel nested sequent proof-search methodology for intuitionistic tense logics (ITLs), supporting finite counter-model extraction. We introduce a new loop-checking method that detects repeating nested sequents using…
Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than…
We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…
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)…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
In the last two decades, there has been much progress on model checking of both probabilistic systems and higher-order programs. In spite of the emergence of higher-order probabilistic programming languages, not much has been done to…
In this paper, we first briefly survey automated termination proof methods for higher-order calculi. We then concentrate on the higher-order recursive path ordering, for which we provide an improved definition, the Computability Path…
We study relationship between first order multiplicative linear logic (MLL1), which has been known to provide representations to different categorial grammars, and the recently introduced extended tensor type calculus (ETTC). We identify a…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
Retrieval-augmented generation (RAG) enhances large language models by grounding outputs in retrieved knowledge. However, existing RAG methods including graph- and hypergraph-based approaches treat retrieved evidence as an unordered set,…
In recent papers we have studied refined enumerations of alternating sign matrices with respect to a fixed set of top and bottom rows. The present paper is a first step towards extending these considerations to alternating sign matrices…
We present team semantics for two of the most important linear and branching time specification languages, Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). With team semantics, LTL is able to express hyperproperties, which have…
State-of-the-art performance in QA tasks is currently achieved by systems employing Large Language Models (LLMs), however these models tend to hallucinate information in their responses. One approach focuses on enhancing the generation…
We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…