Artem Davydov

On the calculus of positively constructed formulas for automated theorem proving

The paper deals with an expressive logic language LF and its calculus. Formulas of this language consist of some large-scale structural elements, such as type quantifiers. The language LF contains only two logic symbols—∀ and ∃, which form the set of logic connectives of the language. The logic calculus JF and complete strategy for automated proof search based on a single unary rule of inference are considered. This calculus has a number of other features which lead to the reduction of the combinatorial complexity of finding the deductions in comparison to the known systems for automated theorem proving as the Resolution method and Genzen calculus. Problems of effective implementation of JF as a program system for automated theorem proving are considered.

Intelligent control via new efficient logics

Abstract An approach to devising the upper level of control systems for multiagent systems has been developed. Problems related to automation of action planning, including those bound up with the mode of cooperative mission performance, are considered. A new efficient logic apparatus for intelligent control is proposed.

Software for automated theorem proving based on the calculus of positively constructed formulas

A description of the calculus of positively constructed formulas (PCF) and prover based on this calculus is considered. The PCF calculus has been developed by Russian scientists S.N. Vassiliev and A.K. Zherlov by an evolutionary way in describing and solving control theory problems. This calculus has features, which are applicable in control theory. The described implementation of the prover uses several techniques and strategies to improve prover performance. The prover is being tested by means of solving problems from TPTP library. The usage of implemented inference search strategies is also commented in this paper.

The formal description of discrete-event systems using positively constructed formulas

The approach to the first-order logic formalization of discrete-event systems based on the positively constructed formulas calculus is presented. Main concepts of the calculus are given and an example of logical deductions which model the behavior of a discrete-event system under supervisory control is presented.

Intelligent control of autonomous underwater vehicles groups

The paper highlights some approaches to fundamental problems of intelligent control of autonomous underwater vehicles (AUV) groups: logic-based approach to task management for inspection and protection of the water area, discrete-event approach to decentralized prioritized distribution of AUVs, hybrid evolutionary models and algorithms for dynamic mission planning, and methods for rigorous analysis of discrete-continuous models of AUVs formations. Hierarchical three-level architecture of control system is supposed and various models of AUV group functioning at the different control levels are considered.

Positive constructed formulas preprocessing for automatic deduction

The preprocessing of positively-constructed formulas (PCFs) for automatic deduction search algorithms is considered in this paper. A new efficient algorithm for conversion of the predicate calculus language formulas to the language of PCFs and equivalent rules of reducing PCFs, preserving the original heuristic structure of knowledge represented by the formulas of the predicate calculus language, are presented.

An optimal control module of sustainable natural resources consumption control synthesis for decision support systems

We consider optimal control problems solved in the process of decision support implemented as a submodule of a hybrid decision support system (HDSS). The HDSS is devoted to figure out a sustainable consumption of the forest resources in an industrial region. The proposed decision is presented to decision maker as possible scenarios of a modeled object development in the future. The scenarios are generated by a subsystem according to initial value combination obtained from various data sources. The mathematical model as an informational object representation is generated by means of automated reasoning that implements a technique of a model construction. The paper deals with the internals of the HDSS related to optimal control model implementation and its integration into the whole system. A HDSS is tested on the data of forest resources of Irkutsk Region.