Related papers: First-Order Decomposition Trees
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…
First-order knowledge compilation techniques have proven efficient for lifted inference. They compile a relational probability model into a target circuit on which many inference queries can be answered efficiently. Early methods used data…
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…
One can often make inferences about a growing network from its current state alone. For example, it is generally possible to determine how a network changed over time or pick among plausible mechanisms explaining its growth. In practice,…
The purpose of this paper is to give an easy to understand with step-by-step explanation to allow interested people to fully appreciate the power of natural deduction for first-order logic. Natural deduction as a proof system can be used to…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…
Lifted probabilistic inference algorithms exploit regularities in the structure of graphical models to perform inference more efficiently. More specifically, they identify groups of interchangeable variables and perform inference once per…
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…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
A layerwise search in a split-by-edges tree (as defined by Br{\ae}ndeland, 2015) of agiven graph produces a maximum independent set in exponential time. A depth-first search produces an independent set, which may or may not be a maximum, in…
Grounding is the task of reducing a first-order theory and finite domain to an equivalent propositional theory. It is used as preprocessing phase in many logic-based reasoning systems. Such systems provide a rich first-order input language…
Large language models achieve strong reasoning performance, yet existing decoding strategies either explore blindly (random sampling) or redundantly (independent multi-sampling). We propose Entropy-Tree, a tree-based decoding method that…
Self-consistency boosts inference-time performance by sampling multiple reasoning traces in parallel and voting. However, in constrained domains like math and code, this strategy is compute-inefficient because it samples with replacement,…
Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…
We propose a generic framework for establishing the decidability of a wide range of logical entailment problems (briefly called querying), based on the existence of countermodels that are structurally simple, gauged by certain types of…
Courcelle's celebrated theorem states that all MSO-expressible properties can be decided in linear time on graphs of bounded treewidth. Unfortunately, the hidden constant implied by this theorem is a tower of exponentials whose height…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…