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Classical logic has a serious limitation in that it cannot cope with the issues of vagueness and uncertainty into which fall most modes of human reasoning. In order to provide a foundation for human knowledge representation and reasoning in…
Weighted Max-SAT is the optimization version of SAT and many important problems can be naturally encoded as such. Solving weighted Max-SAT is an important problem from both a theoretical and a practical point of view. In recent years, there…
This paper presents a Prolog interface to the MiniSat satisfiability solver. Logic program- ming with satisfiability combines the strengths of the two paradigms: logic programming for encoding search problems into satisfiability on the one…
We propose Future Discriminators for Generation (FUDGE), a flexible and modular method for controlled text generation. Given a pre-existing model G for generating text from a distribution of interest, FUDGE enables conditioning on a desired…
Fuzzy logic programming is an established approach for reasoning under uncertainty. Several semantics from classical, two-valued logic programming have been generalized to the case of fuzzy logic programs. In this paper, we show that two of…
Fusemate is a logic programming system that implements the possible model semantics for disjunctive logic programs. Its input language is centered around a weak notion of stratification with comprehension and aggregation operators on top of…
Firedrake is a new tool for automating the numerical solution of partial differential equations. Firedrake adopts the domain-specific language for the finite element method of the FEniCS project, but with a pure Python runtime-only…
Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are…
The quest for analytical solutions to differential equations has traditionally been constrained by the need for extensive mathematical expertise. Machine learning methods like genetic algorithms have shown promise in this domain, but are…
We present a logical framework to represent and reason about fuzzy optimization problems based on fuzzy answer set optimization programming. This is accomplished by allowing fuzzy optimization aggregates, e.g., minimum and maximum in the…
This paper introduces a propositional encoding for lexicographic path orders in connection with dependency pairs. This facilitates the application of SAT solvers for termination analysis of term rewrite systems based on the dependency pair…
Abstract solvers are a method to formally analyze algorithms that have been profitably used for describing, comparing and composing solving techniques in various fields such as Propositional Satisfiability (SAT), Quantified SAT,…
Taxonomy Expansion, which models complex concepts and their relations, can be formulated as a set representation learning task. The generalization of set, fuzzy set, incorporates uncertainty and measures the information within a semantic…
Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience and computational benefits. We introduce concepts of abstract modules and abstract modular systems to study…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
Dung's famous abstract argumentation frameworks represent the core formalism for many problems and applications in the field of argumentation which significantly evolved within the last decade. Recent work in the field has thus focused on…
We introduce FRAT, a new proof format for unsatisfiable SAT problems, and its associated toolchain. Compared to DRAT, the FRAT format allows solvers to include more information in proofs to reduce the computational cost of subsequent…
This paper describes diff-SAT, an Answer Set and SAT solver which combines regular solving with the capability to use probabilistic clauses, facts and rules, and to sample an optimal world-view (multiset of satisfying Boolean variable…
Fuzzy answer set programming is a declarative framework for representing and reasoning about knowledge in fuzzy environments. However, the unavailability of fuzzy aggregates in disjunctive fuzzy logic programs, DFLP, with fuzzy answer set…
We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems.…