20 research outputs found
O neplatnosti věty o silné standardní úplnosti logiky PiMTL
It is well-known that Hájek s basic fuzzy logic (BL), Lukasiewicz logic, and product logic are not strongly standard complete. On the other hand Esteva and Godo s monoidal t-norm logic (MTL) and its involutive extension IMTL are strongly standard complete. In this paper we show that PiMTL (an extension of MTL by the axioms characteristic of product logic) does not enjoy the strong standard completeness theorem like BL, Lukasiewicz, and product logic
Endomorphisms of Lifted Planning Problems
Classical planning tasks are usually modelled in the PDDL which is a schematic language based on first-order logic. Nevertheless, most of the current planners turn this first-order representation into a propositional one via the grounding process. It is well known that the grounding process may cause an exponential blowup. Therefore it is important to detect which grounded atoms are redundant in a sense that they are not necessary for finding a plan and therefore the grounding process does not need to generate them. This is usually done by a relaxed reachability analysis, which can be improved by employing structural symmetries. Symmetries are bijective self-maps preserving the structure of the PDDL task. In this paper, we introduce a new method which is based on self-maps preserving the structure but which need not be bijective. We call these maps PDDL endomorphisms and we show that they can be used for pruning of redundant objects even if they appear in a reachable atom. We formulate the computation of endomorphisms as a constraint satisfaction problem (CSP) that can be solved by an off-the-shelf CSP solver
Endomorphisms of Classical Planning Tasks
Detection of redundant operators that can be safely
removed from the planning task is an essential technique
allowing to greatly improve performance of planners.
In this paper, we employ structure-preserving maps on labeled transition
systems (LTSs), namely endomorphisms well known from model theory, in order
to detect redundancy. Computing endomorphisms of an LTS induced by a
planning task is typically infeasible, so we show how to compute some of
them on concise representations of planning tasks such as finite domain
representations and factored LTSs.
We formulate the computation of endomorphisms as a constraint satisfaction
problem (CSP) that can be solved by an off-the-shelf CSP solver.
Finally, we experimentally verify that the
proposed method can find a sizeable number of redundant operators on the
standard benchmark set