Related papers: Essential variables and positions in terms
The Sigma formulas of the language of arithmetic express semidecidable relations on the natural numbers. More generally, whenever a totality of objects is regarded as incomplete, the Sigma formulas express relations that are witnessed in a…
Component substitution has numerous practical applications and constitutes an active research topic. This paper proposes to enrich an existing component-based framework--a model with dynamic reconfigurations making the system evolve--with a…
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…
Large language models (LLMs) take sequences of subwords as input, requiring them to effective compose subword representations into meaningful word-level representations. In this paper, we present a comprehensive set of experiments to probe…
Word embeddings capture semantic relationships based on contextual information and are the basis for a wide variety of natural language processing applications. Notably these relationships are solely learned from the data and subsequently…
Building on previous work by Andr\'e Platzer, we present a formal language for Stochastic Differential Dynamic Logic, and define its semantics, axioms and inference rules. Compared to the previous effort, our account of the Stochastic…
This paper develops a unified identification framework for counterfactual analysis in incomplete models characterized by support and moment restrictions. I demonstrate that identifying structural parameters and conducting counterfactual…
We develop a system for solving logical deduction one-dimensional ordering problems by transforming natural language premises and candidate statements into first-order logic. Building on Heim and Kratzer's syntax-based compositional…
Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $\Sigma$ of the random vector as the sum of a…
We investigate the integration of word embeddings as classification features in the setting of large scale text classification. Such representations have been used in a plethora of tasks, however their application in classification…
In this paper we provide an alternative semantics for Equilibrium Logic and its monotonic basis, the logic of Here-and-There (also known as G\"odel's G3 logic) that relies on the idea of "denotation" of a formula, that is, a function that…
Tableaux originate as a decision method for a logical language. They can also be extended to obtain a structure that spells out all the information in a set of sentences in terms of truth value assignments to atomic formulas that appear in…
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
Various concepts of grammatical compositionality arise in many theories of both natural and artificial languages, and often play a key role in accounts of the syntax-semantics interface. We propose that many instances of compositionality…
In this paper, a new kind of soft sets related with some common decision making problems in real life called central soft sets is introduced. Properties of some basic operations on central soft sets are shown. It is investigated that some…
We present a framework which constructs an event-style dis- course semantics. The discourse dynamics are encoded in continuation semantics and various rhetorical relations are embedded in the resulting interpretation of the framework. We…
We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. We then show that when compositional semantics is…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…
Definite descriptions are phrases of the form 'the $x$ such that $\varphi$', used to refer to single entities in a context. They are often more meaningful to users than individual names alone, in particular when modelling or querying data…