Related papers: Indexed linear logic and higher-order model checki…
We examine the relationship of graded (multi)modal logic to counting (multichannel) message passing automata with applications to the Weisfeiler-Leman algorithm. We introduce the notion of graded multimodal types, which are formulae of…
We present a formulation of the problem of probabilistic model checking as one of query evaluation over probabilistic logic programs. To the best of our knowledge, our formulation is the first of its kind, and it covers a rich class of…
We present an approach towards the deep, pluralistic logical analysis of argumentative discourse that benefits from the application of state-of-the-art automated reasoning technology for classical higher-order logic. Thanks to its…
Large language models have achieved high performance on various question answering (QA) benchmarks, but the explainability of their output remains elusive. Structured explanations, called entailment trees, were recently suggested as a way…
Curry-Howard correspondences between Linear Logic (LL) and session types provide a firm foundation for concurrent processes. As the correspondences hold for intuitionistic and classic versions of LL (ILL and CLL), we obtain two different…
Despite its success in producing numerous general results on state-based dynamics, the theory of coalgebra has struggled to accommodate the Buechi acceptance condition---a basic notion in the theory of automata for infinite words or trees.…
In this paper we deal with verification of safety properties of term-rewriting systems. The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which further resolved by…
We show that the model-checking problem for successor-invariant first-order logic is fixed-parameter tractable on graphs with excluded topological subgraphs when parameterised by both the size of the input formula and the size of the…
We show that deterministic collapsible pushdown automata of second order can recognize a language that is not recognizable by any deterministic higher-order pushdown automaton (without collapse) of any order. This implies that there exists…
We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term…
Recursive coalgebras provide an elegant categorical tool for modelling recursive algorithms and analysing their termination and correctness. By considering coalgebras over categories of suitably indexed families, the correctness of the…
The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity (or impredicativity) of second and higher order…
We show an approach to automated control of machine vision systems based on incremental creation and evaluation of a particular family of influence diagrams that represent hypotheses of imagery interpretation and possible subsequent…
We consider a regulated multi-class instantaneous matching system with reneging, in which each event requires $K \geq 2$ distinct impatient agents who wait in their respective queues. Each agent class is subject to a buffer capacity,…
The theme of the first two sections, is to prepare the framework of how from a "complicated" family of index models I in K_1 we build many and/or complicated structures in a class K_2. The index models are characteristically linear orders,…
Large Language Models (LLMs) have shown human-like reasoning abilities but still face challenges in solving complex logical problems. Existing unidirectional chaining methods, such as forward chaining and backward chaining, suffer from…
Natural language processing has greatly benefited from the introduction of the attention mechanism. However, standard attention models are of limited interpretability for tasks that involve a series of inference steps. We describe an…
It is well-known that constructing models of higher-order probabilistic programming languages is challenging. We show how to construct step-indexed logical relations for a probabilistic extension of a higher-order programming language with…
We propose trace logic, an instance of many-sorted first-order logic, to automate the partial correctness verification of programs containing loops. Trace logic generalizes semantics of program locations and captures loop semantics by…
In this paper, we present a propositional sequent calculus containing disjoint copies of classical and intuitionistic logics. We prove a cut-elimination theorem and we establish a relation between this system and linear logic.