Related papers: Semantic interpolation
We develop a theory of modulus triples, for future motivic applications.
The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal…
For a division ring $\mathbb F$, the polynomials $f\in\mathbb F$ can be evaluated "on the left" and "on the right" giving rise to left and right Lagrange interpolation problems. The problems containig interpolation conditions of the same…
We present the statistical approach to the combining of signal significances.
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
We discuss an ongoing line of research in the relational (non topological) semantics of non-distributive logics. The developments we consider are technically rooted in dual characterization results and insights from unified correspondence…
Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit…
In this preliminary note, we will illustrate our ideas on automated mechanisms for termination and non-termination reasoning.
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
We prove completeness, interpolation and omitting types for certain predicate topological logics that properly extend the first order case. We aslo count the non isomorphic topological models of a countable theory
The outline of a programme for restructuring mathematical logic. We explain what we mean by "restructuring" and carry out exemplary parts of the programme.
The terms 'semantics' and 'ontology' are increasingly appearing together with 'explanation', not only in the scientific literature, but also in organizational communication. However, all of these terms are also being significantly…
In this work, we show that the complex interpolation space is the same by the two methods.
The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…
Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.
We prove a generalization of Maehara's lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig's interpolation property. As a…
We explore a connection between quantum logic and quantum computing.
This article aims to provide a unified and technical approach to semantic information, communication, and their interplay through the lens of probabilistic logic. To this end, on top of the existing technical communication (TC) layer, we…