Related papers: Puzzles of Existential Generalisation from Type-th…
Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in…
Evidential reasoning is cast as the problem of simplifying the evidence-hypothesis relation and constructing combination formulas that possess certain testable properties. Important classes of evidence as identifiers, annihilators, and…
We argue that the notion of epistemic \emph{possible worlds} in constructivism (intuitionism) is not as the same as it is in classic view, and there are possibilities, called non-predetermined worlds, which are ignored in (classic)…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
We describe the development of a logic for reasoning about specifications in the Edinburgh Logical Framework (LF). In this logic, typing judgments in LF serve as atomic formulas, and quantification is permitted over contexts and terms that…
Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic…
Automatic structures are first-order structures whose universe and relations can be represented as regular languages. It follows from the standard closure properties of regular languages that the first-order theory of an automatic structure…
We take up an idea from the folklore of Answer Set Programming, namely that choices, integrity constraints along with a restricted rule format is sufficient for Answer Set Programming. We elaborate upon the foundations of this idea in the…
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
Doubts are raised concerning the usual interpretation of the alleged failure, by quantum mechanics, of the distributive law of classical logic. The difficulty raised by incompatible sets of observables is overcome within an epistemic…
Descriptive complexity theory aims at inferring a problem's computational complexity from the syntactic complexity of its description. A cornerstone of this theory is Fagin's Theorem, by which a graph property is expressible in existential…
We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put on a set of distinguished relations. We consider restricting a relation to be…
We survey the complexity class $\exists \mathbb{R}$, which captures the complexity of deciding the existential theory of the reals. The class $\exists \mathbb{R}$ has roots in two different traditions, one based on the Blum-Shub-Smale model…
A hierarchy of type universes is a rudimentary ingredient in the type theories of many proof assistants to prevent the logical inconsistency resulting from combining dependent functions and the type-in-type rule. In this work, we argue that…
We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax…
Estimating conditional means using only the marginal means available from aggregate data is commonly known as the ecological inference problem (EI). We provide a reassessment of EI, including a new formalization of identification conditions…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
Existentially closed groups are, informally, groups that contain solutions to every consistent finite system of equations and inequations. They were introduced in 1951 in an algebraic context and subsequent research elucidated deep…
We consider the problem of Partial Quantifier Elimination (PQE). Given formula exists(X)[F(X,Y) & G(X,Y)], where F, G are in conjunctive normal form, the PQE problem is to find a formula F*(Y) such that F* & exists(X)[G] is logically…