The application of graph neural networks (GNNs) to learn heuristic functions in classical planning is gaining traction. Despite the variety methods proposed literature encode tasks for GNNs, a comparative study evaluating their relative performances has been lacking. Moreover, some encodings have assessed solely expressiveness rather than practical effectiveness planning. This paper provides an extensive analysis existing encodings. Our results indicate that smallest encoding based on...

Starting from a decomposition result of monoidal t-norm-based logic (MTL)-chains as ordinal sums, we focus our attention on particular kind indecomposable semihoops, namely weakly cancellative semihoops. The weak cancellation property is proved to be the difference between and pseudocomplementation, so it gives new axiomatization product ΠMTL. By adding this property, some fuzzy logics (propositional first-order) are defined studied obtaining results about their (finite) strong standard...

Abstract It is well known that MTL satisfies the finite embeddability property. Thus complete w. r. t. class of all MTL‐chains. In order to reach a deeper understanding structure this class, we consider extensions by adding generalized contraction since each MTL‐chain form contraction. Simultaneously, also excluded middle laws introduced in [9] and axiom weak cancellation defined [31]. The algebraic counterpart these logics studied characterizing subdirectly irreducible, semisimple, simple...

Abstract Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on study of their counterparts: residuated lattices. Recently, nonassociative generalization (which we call SL) has been studied by Galatos and Ono as logic lattice-ordered unital groupoids. This paper is an alternative Hilbert-style presentation for SL which almost MP -based . then used to obtain, in uniform way applicable most (both associative...

Many efficient algorithms have been designed to recover Nash equilibria of various classes finite games. Special continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite programming. In general, however, are not directly amenable computational procedures. this contribution, we develop an iterative generation technique for finding a equilibrium in whole class two-person zero-sum compact sets. The procedure, which is called the double oracle...

Abstract We prove that the set of formulae provable in full Lambek calculus with structural rule contraction is undecidable. In fact, we show positive fragment this logic

Graph Neural Networks (GNNs) have become the standard method of choice for learning with structured data, demonstrating particular promise in classical planning. Their inherent invariance under symmetries input graphs endows them superior generalization capabilities, compared to their symmetry-oblivious counterparts. However, this comes at cost limited expressive power. Particularly, GNNs cannot distinguish between that satisfy identical sentences C2 logic. To leverage policies PDDL domains,...

Potential heuristics assign a numerical value (potential) to each fact and compute the heuristic for given state as sum of these potentials. A mutex is an invariant stating that certain combination facts cannot be part any reachable state. In this paper, we use mutexes improve potential in two ways. First, show mutex-based disambiguations goal preconditions operators leads less constrained linear program yielding stronger heuristics. Second, utilize construction new optimization functions...

We study the complexity of valued CSP (VCSP, for short) over arbitrary templates, taking general framework integral bounded linearly order monoids as valuation structures. The class problems considered here subsumes and generalizes most common one in VCSP literature, since both monoidal lattice conjunction operations are allowed formulation constraints. Restricting to locally finite monoids, we introduce a notion polymorphism that captures pp-definability style Geiger’s result. As...

Journal Article Solutions to Some Open Problems on Totally Ordered Monoids Get access Rostislav Horčík Institute of Computer Science, Academy Sciences the Czech Republic, Pod Vodárenskou věží 2, 182 07 Prague 8, Republic and Department Mathematics, Faculty Electrical Engineering, Technical University in Prague, Technická 166 27 6, Republic. Search for other works by this author on: Oxford Academic Google Scholar Logic Computation, Volume 20, Issue 4, August 2010, Pages 977–983,...

Abstract This paper investigates a quasi‐variety of representable integral commutative residuated lattices axiomatized by the quasi‐identity resulting from well‐known Wajsberg identity ( p → q ) ≤ if it is written as quasi‐identity, i. e., ≈ 1 ⇒ . We prove that this strictly weaker than corresponding identity. On other hand, we show in fact variety and provide an axiomatization. The obtained results shed some light on structure Archimedean chains. Further, they can be applied to various...

Classical planning tasks are usually modelled in the PDDL which is a schematic language based on first-order logic. Nevertheless, most of current planners turn this representation into propositional one via grounding process. It well known that process may cause an exponential blowup. Therefore it important to detect grounded atoms redundant sense they not necessary for finding plan and therefore does need generate them. This done by relaxed reachability analysis, can be improved employing...