Related papers: Finding Finite Models in Multi-Sorted First Order …
The Weighted First-Order Model Counting Problem (WFOMC) asks to compute the weighted sum of models of a given first-order logic sentence over a given domain. The boundary between fragments for which WFOMC can be computed in polynomial time…
Resolution modulo is a first-order theorem proving method that can be applied both to first-order presentations of simple type theory (also called higher-order logic) and to set theory. When it is applied to some first-order presentations…
We present two different methods for estimating the cost of solving SAT problems. The methods focus on the online behaviour of the backtracking solver, as well as the structure of the problem. Modern SAT solvers present several challenges…
Certain constructs allowed in Mizar articles cannot be represented in first-order logic but can be represented in higher-order logic. We describe a way to obtain higher-order theorem proving problems from Mizar articles that make use 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…
Combining first-order logic and probability has long been a goal of AI. Markov logic (Richardson & Domingos, 2006) accomplishes this by attaching weights to first-order formulas and viewing them as templates for features of Markov networks.…
We investigate lifted inference on ordered domains with predecessor relations, where the elements of the domain respect a total (cyclic) order, and every element has a distinct (clockwise) predecessor. Previous work has explored this…
Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…
We present a unified deductive verification framework for first-order temporal properties based on well-founded rankings, where verification conditions are discharged using SMT solvers. To that end, we introduce a novel reduction from…
Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…
This paper develops a measure for bounding the performance of AND/OR search algorithms for solving a variety of queries over graphical models. We show how drawing a connection to the recent notion of hypertree decompositions allows to…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…
Full first order linear logic can be presented as an abstract logic programming language in Miller's system Forum, which yields a sensible operational interpretation in the 'proof search as computation' paradigm. However, Forum still has to…
Sorting networks are oblivious sorting algorithms with many practical applications and rich theoretical properties. Propositional encodings of sorting networks are a key tool for proving concrete bounds on the minimum number of comparators…
Semantic parsing is the task of obtaining machine-interpretable representations from natural language text. We consider one such formal representation - First-Order Logic (FOL) and explore the capability of neural models in parsing English…
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…
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…
A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307…
Multi-hop reasoning, which requires multi-step reasoning based on the supporting documents within a given context, remains challenging for large language models (LLMs). LLMs often struggle to filter out irrelevant documents within the…
We compare the expressiveness of two extensions of monadic second-order logic (MSO) over the class of finite structures. The first, counting monadic second-order logic (CMSO), extends MSO with first-order modulo-counting quantifiers,…