PC<sub><</sub>, EPC<sub><</sub>, And The Equality Predicate And Subsumption In Resolution-Based Automatic-Theorem-Proving: The First Four Axioms

In this paper we show that the standard notions of tautology and subsumption can be naturally generalized, (so that refutation completeness is preserved with respect to the associated deletion), within the context of (a specified set of) modified deduction rules for binary clausal resolution-refutation which build-in the reflexivity, symmetry, transitivity and predicate substitutivity axioms for equality. To this end, first a resolution system, PC! , in which equality has no special status, is introduced and its refutation completeness under subsumption and tautology deletion shown. The generalized notions of subsumption and tautology, \Sigma 0 -subsumption and \Sigma 0 -tautology , respectively, are then formulated and analyzed. EPC! , a system which provides an adequate deductive context for refutation completeness under deletion with respect to these generalized notions, is then introduced. To prove this completeness, some technical notions (principally, to allow an induction) are i..

Logic Control via Automatic Theorem Proving: COCOLOG Fragments Implemented in Blitzensturm 5.0

The COCOLOG system is a partially ordered family of first order logical theories that describe the controlled evolution of the state of a given partially observered finite machine M. Following the review of the general theory of COCOLOG, the notion of Markovian fragments MTh k ,k 1, of full COCOLOG theories Th k is presented. These fragments enjoy the property of having axiom set of fixed size over time. MTh k and Th k have the virtually same state estimation and control power. Next, a newly developed automatic theorem proving software called Blitzenstrum is described and some applications Blitzenstrum 5.0 to the logic control of a stylized elevator problem are presented

An Approach To The Problems Of Complexity And Hierarchy With An Application To A Detection Problem

this paper, we present and illustrate a formulation of the hierarchical decomposition of the information pattern and control structure of controlled dynamical systems in the case of discrete time finite machines. It rests upon the notion of dynamical consistency which is defined in Section 2.1 below. No optimality properties have, as yet, been established for the formulation given in this paper. However, it leads to a hierarchical decomposition of the trajectory control task which possesses certain efficiency properties in terms of (i) the transmission of observation and control signals and (ii) the computation of trajectories between any specified states. Furthermore, it fits common sense perceptions of the nature of hierarchical command structures. Intuitively, the control commands generated at any level of a hierarchical system constitute control problems; these are to be solved by a control agent of a system at a lower level in the hierarchy; moreover, by the very construction of the hierarchy, the higher level agent is assured that the control problem is indeed solvable by the lower level agent. As we have demonstrated elsewhere [10], our formulation of hierarchical control fits the denotational properties of formal languages. This latter aspect permits the exploitation of the syntactic properties of COCOLOG (conditional observer and controller logic [3], [2]) controllers in the context of hierarchical systems. This corresponds to the idea that a symbol used by a high level agent represents a set of events, states, commands or control problems of a lower level agent. (The customary use of the real and complex number system, functions, operators, etc, in conventional control theory does not exhibit this denotational feature.) In addition, the logical language in whi..