Related papers: Intensional FOL: Many-Sorted Extension
Selectional preference learning methods have usually focused on word-to-class relations, e.g., a verb selects as its subject a given nominal class. This paper extends previous statistical models to class-to-class preferences, and presents a…
The purpose of this paper is to explore some semantic problems related to the use of linguistic ontologies in information systems, and to suggest some organizing principles aimed to solve such problems. The taxonomic structure of current…
A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the order-type of the natural numbers -- we call such a linear extension a…
Modular logic programs provide a way of viewing logic programs as consisting of many independent, meaningful modules. This paper introduces first-order modular logic programs, which can capture the meaning of many answer set programs. We…
This paper proposes a method to translate multilevel flow modeling (MFM) into a first-order language (FOL), which enables the utilisation of logical techniques, such as inference engines and abductive reasoners. An example of this is a…
It was recently shown that arbitrary first-order models canonically extend to models (of the same language) consisting of ultrafilters. The main precursor of this construction was the extension of semigroups to semigroups of ultrafilters, a…
In-context learning (ICL) enables large language models to perform new tasks by conditioning on a sequence of examples. Most prior work reasonably and intuitively assumes that which examples are chosen has a far greater effect on…
The meaning of polysemous words often varies in a highly productive yet predictable way. Generalizing the regularity between conventional senses to derive novel word meaning is crucial for automated processing of non-literal language uses…
First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type…
Poor information retrieval performance has often been attributed to the query-document vocabulary mismatch problem which is defined as the difficulty for human users to formulate precise natural language queries that are in line with the…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
The use of model such as LEL (Lexicon Extended Language) in natural language is very interesting in Requirements Engineering. But LEL, even if it is derived from the Universe of Discourse (UofD) does not provide further details on the…
We present an illative system I_s of classical higher-order logic with subtyping and basic inductive types. The system I_s allows for direct definitions of partial and general recursive functions, and provides means for handling functions…
Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…
Large language models (LLMs) often map semantically related prompts to similar internal representations at specific layers, even when their surface forms differ widely. We show that this behavior can be explained through Iterated Function…
Intensional sets are sets given by a property rather than by enumerating their elements. In previous work, we have proposed a decision procedure for a first-order logic language which provides Restricted Intensional Sets (RIS), i.e., a…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities,…
In this note we suggest that difficulties encountered in natural language semantics are, for the most part, due to the use of mere symbol manipulation systems that are devoid of any content. In such systems, where there is hardly any link…
We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation…