Related papers: Polarizing Double Negation Translations
We propose an algorithm for answering conjunctive queries with negation, where the negated relations have bounded degree. Its data complexity matches that of the best known algorithms for the positive subquery of the input query and is…
We introduce the bilingual dual-coding theory as a model for bilingual mental representation. Based on this model, lexical selection neural networks are implemented for a connectionist transfer project in machine translation. This lexical…
We introduce POLAR - a framework that adds interpretability to pre-trained word embeddings via the adoption of semantic differentials. Semantic differentials are a psychometric construct for measuring the semantics of a word by analysing…
This dissertation explores the roles of polarities and focussing in various aspects of Computational Logic. These concepts play a key role in the the interpretation of proofs as programs, a.k.a. the Curry-Howard correspondence, in the…
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…
This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is…
The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short…
The left-corner transform removes left-recursion from (probabilistic) context-free grammars and unification grammars, permitting simple top-down parsing techniques to be used. Unfortunately the grammars produced by the standard left-corner…
Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
We offer the proofs that complete our article introducing the propositional calculus called semi-intuitionistic logic with strong negation.
We describe a new method of finding interpolants for classical logic using certain refutation system as a starting point. Refutation can be thought of as an alternative approach to the analysis of formal systems: instead of focusing on…
Boolean grammars generalize context-free rewriting by extending the possibilities when dealing with different rules for the same nonterminal symbol. By allowing not only disjunction (as in the case of usual context-free grammars), but also…
One way of proving theorems in modal logics is translating them into the predicate calculus and then using conventional resolution-style theorem provers. This approach has been regarded as inappropriate in practice, because the resulting…
Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…
We present a calculus providing a Curry-Howard correspondence to classical logic represented in the sequent calculus with explicit structural rules, namely weakening and contraction. These structural rules introduce explicit erasure and…
The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to…
Multilingual sentence representations from large models encode semantic information from two or more languages and can be used for different cross-lingual information retrieval and matching tasks. In this paper, we integrate contrastive…
We refute the conjecture that all negative translations are intuitionistically equivalent by giving two counterexamples. Then we characterise the negative translations intuitionistically equivalent to the usual ones.
In this work, we reimagine classical probing to evaluate knowledge transfer from simple source to more complex target tasks. Instead of probing frozen representations from a complex source task on diverse simple target probing tasks (as…