Related papers: First-order logic with incomplete information

In a standard possibilistic logic, prioritized information are encoded by means of weighted knowledge base. This paper proposes an extension of possibilistic logic for dealing with partially ordered information. We Show that all basic…

The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…

The primary purpose of this article is to show that a certain natural set of axioms yields a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely)…

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

We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…

We present a unified categorical treatment of completeness theorems for several classical and intuitionistic infinitary logics with a proposed axiomatization. This provides new completeness theorems and subsumes previous ones by G\"odel,…

First-order multiplicative intuitionistic linear logic (MILL1) can be seen as an extension of the Lambek calculus. In addition to the fragment of MILL1 which corresponds to the Lambek calculus (of Moot & Piazza 2001), I will show fragments…

In this paper we present the first-order logic QLETF+, a quantified version of the logic LETF+, introduced in Coniglio and Rodrigues (Studia Logica 112:561-606, 2024). QLETF+ exhibits several properties that are not always enjoyed by logics…

Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis (1973) earlier considered such a notion of relative likelihood in the…

In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.

In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of…

We extend the logical categories framework to first order modal logic. In our modal categories, modal operators are applied directly to subobjects and interact with the background factorization system. We prove a Joyal-style representation…

Similarity in formal argumentation has recently gained attention due to its significance in problems such as argument aggregation in semantics and enthymeme decoding. While existing approaches focus on propositional logic, we address the…

An algorithm to compute the set of prime implicates of a quantifier-free clausal formula X in first order logic had been presented in earlier work. As the knowledge base X is dynamic, new clauses are added to the old knowledge base. In this…

We study Two-Variable First-Order Logic, FO2, under semantic constraints that model hierarchically structured data. Our first logic extends FO2 with a linear order < and a chain of increasingly coarser equivalence relations E_1, E_2, ... .…

This thesis details a class of partial orders on the space of probability distributions and the space of density operators which capture the idea of information content. Some links to domain theory and computational linguistics are also…

We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…

First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…

We consider the evaluation of first-order queries over classes of databases with bounded expansion. The notion of bounded expansion is fairly broad and generalizes bounded degree, bounded treewidth and exclusion of at least one minor. It…

We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…