Encoding of Planning Problems and Their Optimizations in Linear Logic

We introduce Horn linear logic as a comprehensive logical system capable of handling the typical AI problem of making a plan of the actions to be performed by a robot so that he could get into a set of final situations, if he started with a certain initial situation. Contrary to undecidability of propositional Horn linear logic, the planning problem is proved to be decidable for a reasonably wide class of natural robot systems.The planning problem is proved to be EXPTIME-complete for the robot systems that allow actions with non-deterministic effects. Fixing a finite signature, that is a finite set of predicates and their finite domains, we get a polynomial time procedure of making plans for the robot system over this signature.The planning complexity is reduced to PSPACE for the robot systems with only pure deterministic actions.As honest numerical parameters in our algorithms we invoke the length of description of a planning task ‘from W to Z˜’ and the Kolmogorov descriptive complexity of AxT, a set of possible actions.

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A rewriting framework and logic for activities subject to regulations

Mathematical Structures in Computer Science ◽

10.1017/s096012951500016x ◽

2015 ◽

Vol 27 (3) ◽

pp. 332-375 ◽

Cited By ~ 7

Author(s):

MAX KANOVICH ◽

TAJANA BAN KIRIGIN ◽

VIVEK NIGAM ◽

ANDRE SCEDROV ◽

CAROLYN TALCOTT ◽

...

Keyword(s):

Human Error ◽

Linear Logic ◽

Formal Semantics ◽

Time Constraints ◽

Negative Consequences ◽

Initial State ◽

Goal State ◽

Model Based ◽

Compliance Problem ◽

Planning Problems

Activities such as clinical investigations (CIs) or financial processes are subject to regulations to ensure quality of results and avoid negative consequences. Regulations may be imposed by multiple governmental agencies as well as by institutional policies and protocols. Due to the complexity of both regulations and activities, there is great potential for violation due to human error, misunderstanding, or even intent. Executable formal models of regulations, protocols and activities can form the foundation for automated assistants to aid planning, monitoring and compliance checking. We propose a model based on multiset rewriting where time is discrete and is specified by timestamps attached to facts. Actions, as well as initial, goal and critical states may be constrained by means of relative time constraints. Moreover, actions may have non-deterministic effects, i.e. they may have different outcomes whenever applied. We present a formal semantics of our model based on focused proofs of linear logic with definitions. We also determine the computational complexity of various planning problems. Plan compliance problem, for example, is the problem of finding a plan that leads from an initial state to a desired goal state without reaching any undesired critical state. We consider all actions to be balanced, i.e. their pre- and post-conditions have the same number of facts. Under this assumption on actions, we show that the plan compliance problem is PSPACE-complete when all actions have only deterministic effects and is EXPTIME-complete when actions may have non-deterministic effects. Finally, we show that the restrictions on the form of actions and time constraints taken in the specification of our model are necessary for decidability of the planning problems.

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Advances in Linear Logic

10.1017/cbo9780511629150 ◽

1995 ◽

Cited By ~ 59

Keyword(s):

Linear Logic

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Production management of standardized products using electronic process automation — single window

Automation. Modern Techologies ◽

10.36652/0869-4931-2020-74-8-339-345 ◽

2020 ◽

Keyword(s):

Programming Languages ◽

Production Management ◽

Work Place ◽

Web Interface ◽

Process Automation ◽

Control Programs ◽

New Information ◽

Shift Report ◽

Planning Problems ◽

Registration Card

A non-standard approach to solving the activation planning problems of the standardized products in a multinomenclature workshop is considered. This approach is caused by writing control programs and developing new information systems without changing previously developed workstations, which were created by using an outdated programming languages, in particular Clipper applications. The concept of creating a single information space — a set of databases and software tools integrated at the software level is proposed. Keywords standardized product; normal; software; web interface; single window; automatic work place; production task; shift task; order-shift report; control and registration card

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