相关论文: On cascade products of answer set programs

Traditional Answer Set Programming (ASP) rests upon one-shot solving. A logic program is fed into an ASP system and its stable models are computed. The high practical relevance of dynamic applications led to the development of multi-shot…

Complex systems of systems (SoS) are characterized by multiple interconnected subsystems. Typically, each subsystem is designed and analyzed using methodologies and formalisms that are specific to the particular subsystem model of…

In recent years, Answer Set Programming (ASP), logic programming under the stable model or answer set semantics, has seen several extensions by generalizing the notion of an atom in these programs: be it aggregate atoms, HEX atoms,…

Logic-based argumentation is a well-established formalism modelling nonmonotonic reasoning. It has been playing a major role in AI for decades, now. Informally, a set of formulas is the support for a given claim if it is consistent,…

We introduce heap automata, a formalism for automatic reasoning about robustness properties of the symbolic heap fragment of separation logic with user-defined inductive predicates. Robustness properties, such as satisfiability,…

Answer-set programming (ASP) is a successful problem-solving approach in logic-based AI. In ASP, problems are represented as declarative logic programs, and solutions are identified through their answer sets. Equilibrium logic (EL) is a…

Patterns are fundamental to human cognition, enabling the recognition of structure and regularity across diverse domains. In this work, we focus on structural repeats, patterns that arise from the repetition of hierarchical relations within…

We develop an inductive proof-technique to generate imperative programs for pointer data structures from behavioural specifications expressed in the Answer Set Programming (ASP) formalism. ASP is a non-monotonic logic based formalism that…

Skew-representable matroids form a fundamental class in matroid theory, bridging combinatorics and linear algebra. They play an important role in areas such as coding theory, optimization, and combinatorial geometry, where linear structure…

These lecture notes present a computation driven pathway from classical complex analysis to the theory of compact Riemann surfaces and their connections to algebraic geometry. The exposition follows a compute first then abstract philosophy,…

The Abstraction and Reasoning Corpus (ARC) is a challenging program induction dataset that was recently proposed by Chollet (2019). Here, we report the first set of results collected from a behavioral study of humans solving a subset of…

Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…

To a finite group G one can associate a tower of wreath products S_n[G]. It is well known that the graded direct sum of the Grothendieck groups of the categories of finite dimensional complex representations of these groups can be given the…

Answer Set Programming (ASP) is a popular declarative programming language for solving hard combinatorial problems. Although ASP has gained widespread acceptance in academic and industrial contexts, there are certain user groups who may…

The design of efficient solutions for abstract argumentation problems is a crucial step towards advanced argumentation systems. One of the most prominent approaches in the literature is to use Answer-Set Programming (ASP) for this endeavor.…

Properties of higher characters are developed and applied to symmetric products and Frobenius algebras. A `constructive' proof of the Gel'fand-Kolmogorov theorem is given. Generalisations of that theorem and the Nullstellensatz to symmetric…

We present a system capable of automatically solving combinatorial logic puzzles given in (simplified) English. It involves translating the English descriptions of the puzzles into answer set programming(ASP) and using ASP solvers to…

In this paper, we propose a set theoretic approach for knowledge representation. While the syntax of an application domain is captured by set theoretic constructs including individuals, concepts and operators, knowledge is formalized by…

The ability to abstract, count, and use System~2 reasoning are well-known manifestations of intelligence and understanding. In this paper, we argue, using the example of the ``Look and Say" puzzle, that although deep neural networks can…

Answer Set Programming (ASP) is a logic-based knowledge representation framework, supporting---among other reasoning modes---the central task of query answering. In the propositional case, query answering amounts to computing cautious…