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Sentence embedding methods have made remarkable progress, yet they still struggle to capture the implicit semantics within sentences. This can be attributed to the inherent limitations of conventional sentence embedding methods that assign…

Understanding inferences and answering questions from text requires more than merely recovering surface arguments, adjuncts, or strings associated with the query terms. As humans, we interpret sentences as contextualized components of a…

Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…

This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…

In dialogical argumentation it is often assumed that the involved parties always correctly identify the intended statements posited by each other, realize all of the associated relations, conform to the three acceptability states (accepted,…

While paragraph embedding models are remarkably effective for downstream classification tasks, what they learn and encode into a single vector remains opaque. In this paper, we investigate a state-of-the-art paragraph embedding method…

A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…

In this paper we study the solvability of the equality negation task in a simple wait-free model where processes communicate by reading and writing shared variables or exchanging messages. In this task, two processes start with a private…

Various tasks, such as summarization, multi-hop question answering, or coreference resolution, are naturally phrased over collections of real-world documents. Such tasks present a unique set of challenges, revolving around the lack of…

Richard Cox [1] set the axiomatic foundations of probable inference and the algebra of propositions. He showed that consistency within these axioms requires certain rules for updating belief. In this paper we use the analogy between…

This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…

Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…

Combining higher-order abstract syntax and (co)induction in a logical framework is well known to be problematic. Previous work described the implementation of a tool called Hybrid, within Isabelle HOL, which aims to address many of these…

Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…

Proposed is a program for what we call Geometric Arithmetic, based on our works on non-abelian zeta functions and non-abelian class field theory. Key words are stability and adelic intersection-cohomology theory.

In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence (premises) entails a hypothesis. Existing methods primarily focus on the end-to-end discriminative version of this task, but…

Dense retrieval has shown promise in the first-stage retrieval process when trained on in-domain labeled datasets. However, previous studies have found that dense retrieval is hard to generalize to unseen domains due to its weak modeling of…

We consider an extension of bi-intuitionistic logic with the traditional modalities from tense logic Kt. Proof theoretically, this extension is obtained simply by extending an existing sequent calculus for bi-intuitionistic logic with…

In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…

Initial Semantics aims at characterizing the syntax associated to a signature as the initial object of some category. We present an initial semantics result for typed higher-order syntax together with its formalization in the Coq proof…