Related papers: A Tableaux Calculus for Ambiguous Quantification

In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…

Labelled tableaux have been a traditional approach to define satisfiability checking procedures for Modal Logics. In many cases, they can also be used to obtain tight complexity bounds and lead to efficient implementations of reasoning…

In this paper we present tableau proof systems for various justification logics. We show that the tableau systems are sound and complete with respect to Mkrtychev models. In order to prove the completeness of the tableaux, we give a…

In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressiveness of a more traditional denotation style. We will formalize a category based type and effect system to…

Current representations used in reasoning steps of large language models can mostly be categorized into two main types: (1) natural language, which is difficult to verify; and (2) non-natural language, usually programming code, which is…

We introduce sound and complete labelled sequent calculi for the basic normal non-distributive modal logic L and some of its axiomatic extensions, where the labels are atomic formulas of the first order language of enriched formal contexts,…

Lexical ambiguity is widespread in language, allowing for the reuse of economical word forms and therefore making language more efficient. If ambiguous words cannot be disambiguated from context, however, this gain in efficiency might make…

A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…

In this paper we investigate further the tableaux system for a deontic action logic we presented in previous work. This tableaux system uses atoms (of a given boolean algebra of action terms) as labels of formulae, this allows us to embrace…

Question processing is a fundamental step in a question answering (QA) application, and its quality impacts the performance of QA application. The major challenging issue in processing question is how to extract semantic of natural language…

In this work we show that the ordering ambiguity on quantization depends on the representation choice. This property is then used to solve unambiguously some particular systems. Finally, we speculate on the consequences for more involved…

Although much has been said about parallelism in discourse, a formal, computational theory of parallelism structure is still outstanding. In this paper, we present a theory which given two parallel utterances predicts which are the parallel…

We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error…

We offer the proofs that complete our article introducing the propositional calculus called semi-intuitionistic logic with strong negation.

Ambiguous questions persist in open-domain question answering, because formulating a precise question with a unique answer is often challenging. Previously, Min et al. (2020) have tackled this issue by generating disambiguated questions for…

Mathematical documents written in LaTeX often contain ambiguities. We can resolve some of them via semantic markup using, e.g., sTeX, which also has other potential benefits, such as interoperability with computer algebra systems, proof…

Ambiguous questions are a challenge for Question Answering models, as they require answers that cover multiple interpretations of the original query. To this end, these models are required to generate long-form answers that often combine…

Questions in open-domain question answering are often ambiguous, allowing multiple interpretations. One approach to handling them is to identify all possible interpretations of the ambiguous question (AQ) and to generate a long-form answer…

We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs,…

This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics…