Related papers: Deriving the Predicate-Argument Structure for a Fr…
Natural language understanding applications such as interactive planning and face-to-face translation require extensive inferencing. Many of these inferences are based on the meaning of particular open class words. Providing a…
While argument mining has achieved significant success in classifying argumentative relations between statements (support, attack, and neutral), we have a limited computational understanding of logical mechanisms that constitute those…
Completeness proofs in categorical semantics usually proceed by building a syntactic category whose composition is given by substitution. For untyped effectful Call-by-Value languages, this runs into a basic obstacle: there is no canonical…
In this paper, we introduce a new family of argument-ranking semantics which can be seen as a refinement of the classification of arguments into skeptically accepted, credulously accepted and rejected. To this end we use so-called social…
Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…
Although unification can be used to implement a weak form of $\beta$-reduction, several linguistic phenomena are better handled by using some form of $\lambda$-calculus. In this paper we present a higher order feature description calculus…
Dung's abstract argumentation theory is a widely used formalism to model conflicting information and to draw conclusions in such situations. Hereby, the knowledge is represented by so-called argumentation frameworks (AFs) and the reasoning…
Argument mining tasks require an informed range of low to high complexity linguistic phenomena and commonsense knowledge. Previous work has shown that pre-trained language models are highly effective at encoding syntactic and semantic…
Choice constructs are an important part of the language of logic programming, yet the study of their semantics has been a challenging task. So far, only two-valued semantics have been studied, and the different proposals for such semantics…
The central role of the lexicon in Meaning-Text Theory (MTT) and other dependency-based linguistic theories cannot be replicated in linguistic theories based on context-free grammars (CFGs). We describe Tree Adjoining Grammar (TAG) as a…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
The regular languages with a neutral letter expressible in first-order logic with one alternation are characterized. Specifically, it is shown that if an arbitrary $\Sigma_2$ formula defines a regular language with a neutral letter, then…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
We analyze the problem of defining well-founded semantics for ordered logic programs within a general framework based on alternating fixpoint theory. We start by showing that generalizations of existing answer set approaches to preference…
Multilinear Grammar provides a framework for integrating the many different syntagmatic structures of language into a coherent semiotically based Rank Interpretation Architecture, with default linear grammars at each rank. The architecture…
In this paper we present a transformation of finite propositional default theories into so-called propositional argumentation systems. This transformation allows to characterize all notions of Reiter's default logic in the framework of…
Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
A theory of data types based on category theory is presented. We organize data types under a new categorical notion of F,G-dialgebras which is an extension of the notion of adjunctions as well as that of T-algebras. T-algebras are also used…
We propose a coreference annotation scheme as a layer on top of the Universal Conceptual Cognitive Annotation foundational layer, treating units in predicate-argument structure as a basis for entity and event mentions. We argue that this…