Related papers: Lifted Inference beyond First-Order Logic
One of the most important queries in knowledge compilation is weighted model counting (WMC), which has been applied to probabilistic inference on various models, such as Bayesian networks. In practical situations on inference tasks, the…
The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the…
Accurately segmenting a citation string into fields for authors, titles, etc. is a challenging task because the output typically obeys various global constraints. Previous work has shown that modeling soft constraints, where the model is…
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for…
Since the 1970s with the work of McNaughton, Papert and Sch\"utzenberger, a regular language is known to be definable in the first-order logic if and only if its syntactic monoid is aperiodic. This algebraic characterisation of a…
Given a set $F$ of words, one associates to each word $w$ in $F$ an undirected graph, called its extension graph, and which describes the possible extensions of $w$ on the left and on the right. We investigate the family of sets of words…
We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of…
I have argued elsewhere that second order logic provides a foundation for mathematics much in the same way as set theory does, despite the fact that the former is second order and the latter first order, but second order logic is marred by…
The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives…
It is known that first-order logic with some counting extensions can be efficiently evaluated on graph classes with bounded expansion, where depth-$r$ minors have constant density. More precisely, the formulas are $\exists x_1 ... x_k \#y…
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
The satisfiability problem for First-order Modal Logic (\FOML) is undecidable even for simple fragments like having only unary predicates, two variables etc. Recently a new way to identify decidable fragments of \FOML has been introduced…
The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…
We introduce a logic called distance neighborhood logic with acyclicity and connectivity constraints ($\mathsf{A\&C~DN}$ for short) which extends existential $\mathsf{MSO_1}$ with predicates for querying neighborhoods of vertex sets and for…
Causal reasoning in relational domains is fundamental to studying real-world social phenomena in which individual units can influence each other's traits and behavior. Dynamics between interconnected units can be represented as an…
A binary relation on graphs is recursively enumerable if and only if it can be computed by a formula in monadic second-order logic. The latter means that the formula defines a set of graphs, in the usual way, such that each "computation…
We formulate a framework for describing behaviour of effectful higher-order recursive programs. Examples of effects are implemented using effect operations, and include: execution cost, nondeterminism, global store and interaction with a…
Standpoint extensions of knowledge representation formalisms have been recently introduced as a means to incorporate multi-perspective modelling and reasoning through modal operators that attribute pieces of knowledge to specific entities…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…