Related papers: Categorial Minimalist Grammar
In this chapter, we introduce a new dialogical system for first order classical logic which is close to natural language argumentation, and we prove its completeness with respect to usual classical validity. We combine our dialogical system…
In formal argumentation, a distinction can be made between extension-based semantics, where sets of arguments are either (jointly) accepted or not, and ranking-based semantics, where grades of acceptability are assigned to arguments.…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
We introduce a subclass of the commutative regular languages that is characterized by the property that the state set of the minimal deterministic automaton can be written as a certain Cartesian product. This class behaves much better with…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
An understandable concrete syntax and a comprehensible abstract syntax are two central aspects of defining a modeling language. Both representations of a language significantly overlap in their structure and also information, but may also…
A non-deterministic call-by-need lambda-calculus \calc with case, constructors, letrec and a (non-deterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of left-most outermost…
We propose a computational modeling framework for inducing combinatory categorial grammars from arbitrary behavioral data. This framework provides the analyst fine-grained control over the assumptions that the induced grammar should conform…
Despite ample evidence that our concepts, our cognitive architecture, and mathematics itself are all deeply compositional, few models take advantage of this structure. We therefore propose a radically compositional approach to computational…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
The mathematical representation of semantics is a key issue for Natural Language Processing (NLP). A lot of research has been devoted to finding ways of representing the semantics of individual words in vector spaces. Distributional…
Dung's abstract argumentation framework consists of a set of interacting arguments and a series of semantics for evaluating them. Those semantics partition the powerset of the set of arguments into two classes: extensions and…
We present a novel technique for learning semantic representations, which extends the distributional hypothesis to multilingual data and joint-space embeddings. Our models leverage parallel data and learn to strongly align the embeddings of…
A categorial grammar assigns one of several syntactic categories to each symbol of the alphabet, and the category of a string is then deduced from the categories assigned to its symbols using two simple reduction rules. This paper…
Combining large language models with logical reasoning enhances their capacity to address problems in a robust and reliable manner. Nevertheless, the intricate nature of logical reasoning poses challenges when gathering reliable data from…
Modelling compositional meaning for sentences using empirical distributional methods has been a challenge for computational linguists. We implement the abstract categorical model of Coecke et al. (arXiv:1003.4394v1 [cs.CL]) using data from…
In this paper, we propose a set theoretic approach for knowledge representation. While the syntax of an application domain is captured by set theoretic constructs including individuals, concepts and operators, knowledge is formalized by…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
A finitary propositional logic can be given an algebraic reading in two different ways: by translating formulas into equations and logical rules into quasi-equations, or by translating logical rules directly into equations. The former type…