相关论文: Deciding Disjunctive Linear Arithmetic with SAT
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…
Nondeterministic Discounted-Sum Automata (NDAs) are nondeterministic finite automata equipped with a discounting factor $\lambda>1$, and whose transitions are labelled by weights. The value of a run of an NDA is the discounted sum of the…
Recursive algebraic data types (term algebras, ADTs) are one of the most well-studied theories in logic, and find application in contexts including functional programming, modelling languages, proof assistants, and verification. At this…
Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical…
We propose a new batch mode active learning algorithm designed for neural networks and large query batch sizes. The method, Discriminative Active Learning (DAL), poses active learning as a binary classification task, attempting to choose…
Many applications require solving sequences of related mixed-integer linear programs. We introduce a class of parametric disjunctive inequalities (PDIs), obtained by reusing the disjunctive proofs of optimality from prior solves to…
Answer set programming is a declarative programming paradigm oriented towards difficult combinatorial search problems. A fundamental task in answer set programming is to compute stable models, i.e., solutions of logic programs. Answer set…
We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…
In the last years, there has been an increasing demand of a variety of logical systems, prompted mostly by applications of logic in AI and other related areas. Labeled Deductive Systems (LDS) were developed as a flexible methodology to…
Bounded fitting is a general paradigm for learning logical formulas from positive and negative data examples, that has received considerable interest recently. We investigate bounded fitting for the description logic ALC and its syntactic…
Bounded fitting is an attractive paradigm for learning logical formulas from labeled data examples that offers PAC-style generalization guarantees and can often be implemented leveraging SAT solvers. It has been successfully applied to…
In this work, we consider the satisfiability problem in a logic that combines word equations over string variables denoting words of unbounded lengths, regular languages to which words belong and Presburger constraints on the length of…
Classical (or Boolean) type theory is the type theory that allows the type inference $\sigma \to \bot) \to \bot => \sigma$ (the type counterpart of double-negation elimination), where $\sigma$ is any type and $\bot$ is absurdity type. This…
In this paper, we compare four different semantics for disjunction in Answer Set Programming that, unlike stable models, do not adhere to the principle of model minimality. Two of these approaches, Cabalar and Mu\~niz' \emph{Justified…
Following the idea of Subexponential Linear Logic and Stratified Bounded Linear Logic, we propose a new parameterized version of Linear Logic which subsumes other systems like ELL, LLL or SLL, by including variants of the exponential rules.…
The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…
Disentangling the explanatory factors in complex data is a promising approach for generalizable and data-efficient representation learning. While a variety of quantitative metrics for learning and evaluating disentangled representations…
Logic programs with ordered disjunction (LPODs) combine ideas underlying Qualitative Choice Logic (Brewka et al. KR 2002) and answer set programming. Logic programming under answer set semantics is extended with a new connective called…
We introduce a tool for analysing models of $\textnormal{CT}^-$, the compositional truth theory over Peano Arithmetic. We present a new proof of Lachlan's theorem that arithmetical part of models of $\textnormal{PA}$ are recursively…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…