Related papers: A general method for deciding about logically cons…
Collective decision making is often a customary action taken in government crowdsourcing. Through ensemble of opinions (popularly known as judgment analysis), governments can satisfy majority of the people who provided opinions. This has…
Opinion formation cannot be modeled solely as an ideological deduction from a set of principles; rather, repeated social interactions and logic constraints among statements are consequential in the construct of belief systems. We address…
A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In…
Approval voting is a common method of preference aggregation where voters vote by ``approving'' of a subset of candidates and the winner(s) are those who are approved of by the largest number of voters. In approval voting, the degree to…
The theory of belief functions is an effective tool to deal with the multiple uncertain information. In recent years, many evidence combination rules have been proposed in this framework, such as the conjunctive rule, the cautious rule, the…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
Traditional belief revision frameworks often rely on the principle of minimalism, which advocates minimal changes to existing beliefs. However, research in human cognition suggests that people are inherently driven to seek explanations for…
We introduce a new logic of graded distributed belief that allows us to express the fact that a group of agents distributively believe that a certain fact holds with at least strength k. We interpret our logic by means of computationally…
We present global convergence rates for a line-search method which is based on random first-order models and directions whose quality is ensured only with certain probability. We show that in terms of the order of the accuracy, the…
Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notions of solutions. Typical examples are satisfying…
One of the most important aspects in any treatment of uncertain information is the rule of combination for updating the degrees of uncertainty. The theory of belief functions uses the Dempster rule to combine two belief functions defined by…
Epistemic uncertainty arises in lack of complete knowledge about the state of a system. There are multiple mathematical frameworks for measuring such uncertainty quantitatively, often referred to as imprecise probability theories. Inspired…
Belief fusion is the principle of combining separate beliefs or bodies of evidence originating from different sources. Depending on the situation to be modelled, different belief fusion methods can be applied. Cumulative and averaging…
In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a three…
Cardinality constraints in optimization are commonly of $L^0$-type, and they lead to sparsely supported optimizers. An efficient way of dealing with these constraints algorithmically, when the objective functional is convex, is…
Newton method is one of the most powerful methods for finding solutions of nonlinear equations and for proving their existence. In its "pure" form it has fast convergence near the solution, but small convergence domain. On the other hand…
The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
Large language models (LLMs) have achieved significant performance in various natural language reasoning tasks. However, they still struggle with performing first-order logic reasoning over formal logical theories expressed in natural…
Constraint propagation algorithms implement logical inference. For efficiency, it is essential to control whether and in what order basic inference steps are taken. We provide a high-level framework that clearly differentiates between…