A formal system of classical analysis

1973 ◽  
pp. 13-27
Author(s):  
Horst Luckhardt
Keyword(s):  
Formal System ◽  
Classical Analysis

Modality and folk psychology

2019 ◽  
Vol 28 (1) ◽  
pp. 19-27
Author(s):  
Ja. O. Petik
Keyword(s):  
Modal Logic ◽  
Brain Activity ◽  
Formal System ◽  
Philosophy Of Logic ◽  
Psychological States ◽  
Formal Systems ◽  
Modern Psychology ◽  
Philosophical Interpretation ◽  
Important Direction

The connection of the modern psychology and formal systems remains an important direction of research. This paper is centered on philosophical problems surrounding relations between mental and logic. Main attention is given to philosophy of logic but certain ideas are introduced that can be incorporated into the practical philosophical logic. The definition and properties of basic modal logic and descending ones which are used in study of mental activity are in view. The defining role of philosophical interpretation of modality for the particular formal system used for research in the field of psychological states of agents is postulated. Different semantics of modal logic are studied. The hypothesis about the connection of research in cognitive psychology (semantics of brain activity) and formal systems connected to research of psychological states is stated.

Retrieval System and Dynamic Algorithm Looking for Axioms of Notions Defined by Programs

1993 ◽  
Vol 19 (3-4) ◽  
pp. 275-301
Author(s):  
Andrzej Biela
Keyword(s):  
Theorem Proving ◽  
Dynamic Process ◽  
Functional Equations ◽  
Automated Theorem Proving ◽  
Retrieval System ◽  
Formal System ◽  
Dynamic Algorithm ◽  
Algorithmic Logic ◽  
Correctness Of Programs

In this paper we shall introduce a formal system of algorithmic logic which enables us to formulate some problems connected with a retrieval system which provides a comprehensive tool in automated theorem proving of theorems consisting of programs, procedures and functions. The procedures and functions may occur in considered theorems while the program of the above mentioned system is being executed. We can get an answer whether some relations defined by programs hold and we can prove functional equations in a dynamic way by looking for a special set of axioms /assumptions/ during the execution of system. We formulate RS-algorithm which enables us to construct the set of axioms for proving some properties of functions and relations defined by programs. By RS-algorithm we get the dynamic process of proving functional equations and we can answer the question whether some relations defined by programs hold. It enables us to solve some problems concerning the correctness of programs. This system can be used for giving an expert appraisement. We shall provide the major structures and a sketch of an implementation of the above formal system.

Extensions of Elementary Cause-Effect Structures

2021 ◽  
Vol 179 (2) ◽  
pp. 93-111
Author(s):  
Ludwik Czaja
Keyword(s):  
Characteristic Feature ◽  
Petri Nets ◽  
Algebraic System ◽  
Formal System ◽  
Parallel Execution

Cause-effect structures are objects of a formal system devised for modeling, testing and verifying properties of tasks, where parallel execution of actions is the most characteristic feature. This is an algebraic system called a quasi-semiring. In this paper elementary cause-effect structures, a system behaviourally equivalent to 1-safe Petri nets, are extended by the following features: weighted edges, multi-valued nodes having capacities (counterpart of place/transition Petri nets), inhibitors and a model of time. The extensions are accomplished by modifying the notion of state and semantics, but leaving unchanged structure of the quasi-semiring expressions.

A Formal System for Proving Some Properties of Programs in Iterative Combinatory Spaces

1984 ◽  
Vol 7 (3) ◽  
pp. 359-365
Author(s):  
Dymiter Skordev
Keyword(s):  
Formal System ◽  
Logical System ◽  
Theoretical Methods ◽  
General Properties ◽  
Space Approach

The paper presents an abstract tool for describing general properties of programs. Iterative combinatory space approach makes possible to transfer recursion – theoretical methods onto logical system which is constructed in this paper.

scholarly journals Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clifford V. Johnson ◽  
Felipe Rosso
Keyword(s):  
Phase Structure ◽  
Scalar Potential ◽  
String Equation ◽  
Two Dimensional ◽  
Leading Order ◽  
Classical Analysis ◽  
First Order ◽  
First Order Phase Transition ◽  
Definition Of ◽  
First Order Phase

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

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