# Tamas GergelyApplied Logic Laboratory | ALL

Tamas Gergely

Professor, PhD, DSc

## About

137

Publications

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333

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Introduction

Tamas Gergely currently works at Applied Logic Laboratory.

Additional affiliations

January 1986 - present

**Applied Logic Laboratory**

Position

- CEO

## Publications

Publications (137)

Today Cognitive computing and Artificial Intelligence (AI) face the same challenges namely, simulate human thought processes and mimic the way human brain works. The main difference between Cognitive computing and AI is: (i) AI models various functions of human intelligence, where computer is one of the modelling means though often the most importa...

The paper discusses a general scheme of constructing different systems of artificial intelligence and data mining. This scheme interprets various intelligent technologies as kinds of reasoning. All of these kinds of reasoning aim to cognition and formation of domain models. We assume that reasoning has a referential character, i.e. reasoning can us...

Background:
Diabetes, a metabolic disorder, has reached epidemic proportions in developed countries. The disease has two main forms: type 1 and type 2. Disease management entails administration of insulin in combination with careful blood glucose monitoring (type 1) or involves the adjustment of diet and exercise level, the use of oral anti-diabet...

Due to demographic changes, European healthcare systems face two serious threats: healthcare delivery may become inadequate to perceived needs of the citizens or the cost may spiral out of control. With the decrease in the labour force, there is an urgent need to make more health services mobile allowing citizens with chronic diseases stay longer i...

In the previous chapter the first results connecting syntactic and semantic constructs were obtained under the assumption
that the modification calculi possess the property of conformability. This property means that there exists a generating rule system which corresponds to the modification rule system of a modification calculus in a special, stri...

In the present section we introduce the tools used to represent the sets of properties in the modification calculi. First
of all we define the definition method for modification rules. Then we define the transformation of modification rules into
generator rules. There will be a wider class of modification calculi defined than the class of atomic mo...

As mentioned, the proposed approach integrates all three types of methodology of investigation: the philosophical–methodological,
the logical–mathematical and the engineering–computational ones. At the formal level of abstraction the approach basically
provides methods and tools in the logical–mathematical spirit. However, at the same time the form...

The objective of the present chapter is the informal introduction of the main notions that will serve as the basis of our
approach for modelling cognitive reasoning. Most of these notions should be well known to readers. However we aim not to give
them a formal definition but to provide an explanation of how these notions will be understood and app...

Pure J logics are the logical basis for the JSM method. Both the modification and the iterative theories built over the St or It logics, respectively, can be suggested for the mathematical representation of various versions of the JSM method

Recently the creation of artificial cognitive systems has been one of the main challenges in the field of information and communication technology. Despite the many alternative approaches a complete and convincing artificial cognitive system has not yet been developed and, even further, it has not been known how to design and build artificial cogni...

In the present chapter appropriate semantics will be developed for the modification calculi as a special type of inference. This semantics will correspond to the intuitive meaning of discrete cognitive processes, sectioned into stages and modules.

Understanding cognition and particularly cognitive reasoning and developing artificial cognizing agents are challenging and long-term research problems. In this book we wish to take a step towards a better understanding of cognitive reasoning processes by developing a scientifically well-founded general approach that provides methods and tools for...

The main purpose of this chapter is to introduce some classes of many-valued logics, namely the class of pure J logic (PJ logics) and two its subclasses: the class of finite pure J logics (FPJ logics) and the class of iterative versions of finite PJ logics.

In this chapter we introduce the first-order logics that correspond to the propositional ones discussed in the previous section. We will consider many-sorted firstorder logics where many-sortedness is significant for the applications further to be discussed.

Here we discuss some open problems connected with the further development of the mathematical theory of the formal CR framework developed in the present book. We present the problems in thematically grouped form.

In this chapter we establish a relationship between validities in L-structures and I-structures, where L is an FPJ logic and I is its iterative version w.r.t. some value τ ∈ 𝓥 (L, |),i.e.I = Iτ(L).

We introduce a formalism that has a dual semantical–syntactical character. Modification calculi contain a collection of statements, practically playing the role of axioms, which identically define a certain canonical model.The representation of this model implicitly affects certain inference rules. Note that, besides some usual inference rules of f...

Let σ be a basic JSM signature and 𝔍 be an L-structure of signature σ, where L is a PJ logic.Then 𝔍 is called a basic JSM-structure (BJSMstructure), if it is a model of the axioms (S1)—(S4) and (SA) of the basic JSM theory.

The imitation of cognitive reasoning will be based on the technique of modification calculi. In this section two classes of
modification calculi will be introduced differing in special syntactical restrictions. We will study the calculi of these
classes and show that any calculus of these classes is conformable and, consequently, correct and comple...

The notion of perfect modification calculi may seem unexpected and abstract, but it is introduced because of the needs arising
from practical applications. Below we provide a fairly simple artificial example for the rule that allows the analysis of
property sets.

The generalised JSM method was proposed as a method that provides finer data analysis than that provided by the simple JSM method. The main supposition of the generalised JSM method is: each possible cause may be associated with a set of its own inhibitors, which interfere with the appearence of effects even if the cause exists. Therefore, we can c...

In this section we study the so-called set sorts. As mentioned above, objects of set sorts are regarded as sets. This is related
to a certain number of restrictions, some of which will be considered below. Note that we will first investigate those sets
of conditions that are technically simple and transparent. Later on our technique will be much mo...

Suppose that we have a situation where the properties themselves are sets, i.e. the elements of the sort 𝖯 are sets. If we
attempt to represent this situation in some versions of the JSM theories then this yields significant changes and complications
in the selected theories. The advantage may be a potential decrease of the computational complexity...

In this chapter we discuss the level of realisation of the proposed CR formalism. We introduce the general scheme (the object
model) of an application program for data analysis by means of the formalised reasonings provided by the formal CR framework.

Here we introduce the cut of arbitrary strings and we discuss a few basic properties of the cuts. In this case we are not
interested in the nature of the elements of a string. Obviously we will use the tools introduced above for working with the
record strings.

At the conceptual level of abstraction the proposed approach provides the conceptual CR framework. In order to characterise
and model the cognitive reasoning processes this framework defines the main actor of cognition, which is the cognizing agent. The structure together with all the constituents and functioning of cognizing agents is represented...

Now we investigate the connection between derivability in modification calculi and validity in L-structures, where L is an FPJ logic. With few exceptions, in this section we will consider only pure inferences in modification calculi, i.e. inferences from own state descriptions of modification calculi. Our tools of investigation
will include

In this chapter we describe the structure, processes, techniques and methods at the conceptual level, which according to our
approach will be necessary (i) to understand (e.g. human) cognition and (ii) to support its modelling. This structure, together
with all the constituents forms, we call a “cognitive architecture”. This architecture will be de...

In this chapter we aim to provide a conceptual theory of cognitive reasoning processes, i.e. processes that permit a cognizing
agent to gain new knowledge.
According to our approach the conceptual model should provide the preparatory stage for the development of the formal theory
of cognitive reasoning. Therefore the main constituents of the forma...

This paper presents an overview on the design and implementation of a computer system for the interpretation of home monitoring data of diabetic patients. The comprehensive methodology covers the major information processing steps leading from raw data to a concise summary of what has happened between two subsequent visits. It includes techniques f...

Chronic care consists of a sequence of actions to treat a specific clinical disorder over time as a function of the ways in which illness progresses and patients respond to management actions. Outcomes depend on physicians' skills to select the actions best suited for their patients and competent self-management. This paper presents the architectur...

Recent advances in information and communication technology allow the design and testing of new models of diabetes management, which are able to provide assistance to patients regardless of their distance from the health care providers. The M2DM project, funded by the European Commission, has the specific aim to investigate the potential of novel t...

Inductive sorting GMDH algorithms can be used as neurons in the multilayered neural network for solution of interpolation type problems of artificial intelligence (such as pattern recognition, laws discovery, step-wise random processes prediction and another) for noise filtration, unknown factors discovery and data mining. This approach can discove...

A neural network model that may give phase synchronization of activity patterns in ensembles with different types of complexity is described and simulated. This model is used to study the dynamic behavior of coupled phase oscillators with cosine interaction between them. Different schemes of the network architecture such as mean-field and nearest-n...

Non-equilibrium dynamics of ensemble consisting of interacting Josephson-like elements with lateral excitatory and inhibitory couplings is studied analytically and by computer simulation. For this model an extremely rich and unusual dynamic behavior (long-term and short-term metastable states, modulated limit cycles and strange attractors) is obser...

The method of synchronization of activity patterns in different neural structures is considered, the approach developed here may be used for modelling of the co-operative processes in physics, chemistry, and biology as well as the processes of pattern formation and pattern recognition by oscillatory neural networks. It was shown that oscillatory dy...

Intelligent control is connected with open problem domains that
characterize control situations. Therefore, the formalization of problem
situations, uncertainty handling and efficient problem solving methods
are important to realise this control. A formal theory of plausible
reasoning is introduced which provides an appropriate foundation for
intel...

The main direction in modern imaging is increasing the spatial resolution and selectivity for pathology
pattern recognition at the microscale. Dynamic optical imaging (DOl) has enormous potential in the selectivity
of description of living tissue state at cellular and subcellular levels. However, multiple light
scattering creates considerable diffi...

The dynamical behaviour of neural networks consisting of excitatory and inhibitory neuron populations, dynamic pattern formation related to neural oscillation and stochastic modelling of memory search are considered. The memory search is based on the input-output interrelations in the network and is determined by the transitions between different s...

The possibility is considered for revealing and identifying pathology through the spatially distributed low amplitude dynamic optical contrasts, which reflect the physiological dynamics of the living tissue. A simple conventional CCD-based system and software for optical image sequence processing are described. Examples of the application of this a...

The processes of self-organization in neural networks with homogeneous and heterogeneous structures of synaptic connections between neurons are studied and the dynamic behaviour of neural network driven by external noise is analyzed. The Wilson-Cowan type equations for the excitatory' and inhibitory activities with some modifications are used. The...

Mathematical Background.- 1. Logic and Model Theory.- 2. Inductive Definability.- I Computability.- 3. Introduction to Part I.- 4. Main Properties of Program Schemas.- 5. Extension of Program Schemas.- 6. Program Schemas with Stacks.- 7. Computability.- 8. On Inductive Definability of 1- and 2-Computable Relations.- II Extended Dynamic Logics.- 9....

Programs operate on their data environments. If we are interested in the change caused by the execution of a program in its environment then the input-output semantics, defined as a binary relation on data sequences, is suitable. A great variety of program properties is connected with the relational semantics, e.g. partial correctness, quasi-total...

Besides the description of program properties, programming logics are also expected to provide appropriate tools for proving the existence of these properties at concrete programs. Therefore, an appropriate calculus is required to permit the proof of formulas of the descriptive language. Moreover, we expect this calculus to be realizable in some in...

Temporal logic investigated in the previous part represents program execution by taking trace semantics into account. The traces are represented by the changes of local variables. The computational paths are realized according to the time structure of the temporal logic. Note that for a given program p the set Trace
A
. 〚p〛 of traces in a given mod...

In order to develop a flexible and powerful programming theory an appropriate formal theory is required which permits us to define all the objects and notions necessary for the theoretical characterization of programs and programming languages in a uniform way. The required formal theory can be ensured by an appropriate definition theory which allo...

Having formally defined the notions of programs and their executions over the abstract models of computers it is an important question how programs can be characterized. The first possibility is to consider how the programs are built up , i.e. what programming constructs participate in their definitions and how. The number of cycles or the number o...

As is well known, temporal logic can be defined in dynamic logic (ef. Harel [1984]) in the propositional case. This fact was used by Meyer [1980] when he stated that temporal logic is uninteresting from a scientific point of view.

Temporal logic as a descriptive language allows us to formalize our expectations about the time during which a program runs. Since different program verification methods differ in their view of how they consider program execution we can characterize them axiomatically by using temporal logic. In this chapter we give the required characterization fo...

Temporal logic is based on modal logic which uses the standard two modalities □ and ◊ interpreted as “necessity” and “possibility”. Kripke [1963] elaborated a formal semantics for modal logic. Prior [1957] first suggested a temporal interpretation of the modalities, “always” for □ and “sometimes” for ◊. Following von Wright [1965] a new modality, t...

We have seen so far how the programming language r P
σ
can be augmented with new computational devices by the use of extension. From the viewpoint of computational power, as in Chapter 5, it is sufficient to augment the language r P
σ
with stacks. Therefore, for the theory it is sufficient to use the stack extension of r P
σ
. However, the way the...

The development of a programming logic in the scope of classical first -order logic is connected with making the formal notions, used to describe program properties, internal. This can be ensured by defining the definability of these notions in the logic in question. Here we show how dynamic logic can be developed in classical first-order logic by...

As we have seen, the σ-type dynamic logic and even its Floyd-Hoare sublanguage are incomplete. The efforts made in the previous chapter to make dynamic logic complete did not bring us pragmatically satisfactory results. Therefore, we now look for another way to obtain a pragmatically satisfactory complete dynamic logic. First of all we require that...

The basic programming language introduced so far should be considered as the minimal language in our investigation. It is sufficient for a programming logic to establish only some negative results by showing that something fails even in the case of this minimal language. However, for a programming logic we need a programming language which is unive...

Our main objective in this part is the development of a theory based on classical first-order logic which can serve as the foundation for a logic-based programming theory. Namely, this theory should deal with programs and with their logically meaningful semantics, and should also provide purely logical tools to extend programming languages with new...

The theory of computability deals with the formal characterization of the “effectively Computable” functions and relations. Different pieces of machinery, such as recursive functions, register machines, and normal algorithms, have been proposed for this aim . Programming languages provide a new technique for the formalization of computability, and...

In the previous part, temporal logic was introduced to describe program properties. For this logic, traditional modal logic with a temporal interpretation of the modalities was augmented with two kinds of variables, global and local. The use of local variables allows us to describe and characterize the program execution. However, as observed in Wol...

Up to now we have developed different logical tools in order to describe and investigate programming languages. However, from the logical viewpoint the programming languages remained external with respect to the logic, by the use of which the investigation took place . This raises an interesting question. Is it possible to give purely logical objec...

In this chapter we complete the investigation of the interrelation of temporal and dynamic logics by showing that they are incomparable. For this we have to prove that temporal logic cannot define dynamic logic.

The first significant steps in developing a unique logically based programming theory have been made in Part 1. These steps resulted in a computation theory in the scope of first-order classical logic. To accomplish the development of our programming theory we have to make efforts to develop appropriate tools with the same scope to deal with the ch...

Developing a logic-based theory of programming, the chief concern is the logical definition of the main notions connected with programming. In order to deal successfully with this concern an appropriate definability theory has to be used . In our program-theoretic investigation, inductive definability will play a significant role in the establishme...

Countable models play a significant role in programming theory from a pragmatic point of view, since programs are executed in countable models (e.g. on integers). Therefore it is interesting to study the relationship between the two logics in question with respect to the enumerable models. One may expect either that the results of the above chapter...

The programming theory to be developed in this work is based on first-order classical logic. In order to follow this development we expect the reader to be familiar with the elements of classical mathematical logic and with the basic notions of (naive) set theory that we accept as our starting point.

Now let us see how the σ-type temporal logic ML
σ
can be used to reason about programs and how program properties can be described. The temporal logic of programs will not mention programs explicitly, but it will operate on the computational paths realizing the execution of a program. This is one of the fundamental differences between the viewpoint...

In this chapter we introduce a basic programming language by defining its syntax and semantics. The syntax is defined as a set of program schemas constructed with a given set of program constructs by using the terms and the open formulas of a fixed alphabet (similarity type). This ensures that the function and relation symbols from which the terms...

As we have seen, dynamic logic is based on input-output relational semantics. The expressive power of this descriptive language permits us to define many different program properties, including those connected with the “history” of execution. In order to characterize program semantics in this language, a computer is modelled by the data environment...

In this chapter we show how an appropriate first-order language can be built up to describe the properties of rP
σ1 -programs. Here we also use the logical tools introduced in Chapter 13, and the method of the development of the required dynamic logics is similar to that used in the previous chapter. We have proved in Part I that rP
σ1≈I for a one-...

With the time logic introduced in the previous chapter we have three languages for supporting programming theory. How are these languages related to each other? We show in the present chapter that time logic is the most powerful in expressive power. This will be shown by embedding the other two languages, i.e. temporal and dynamic logics, into time...

In the book a Prolog based discrete-continous simulation language (CS-Prolog) is introduced and some applications are presented.

Medical expert systems which support the setting of diagnosis usually realize statistic diagnostic methods obtained by elicitating expert’s knowledge. However, these systems realize a fenomenological approach by imitating only the “surface” of the expert’s thinking when setting a diagnosis, instead of considering a causal thinking process that aims...

As with other disciplines computers are conquering the field of FLT though following the traditional teaching methods of those disciplines despite the fact that language is a natural entity. Therefore language teaching should aim at conditioning this development. In the paper we outline an approach to serve the development of constructive models fo...

Inductive reasoning is an important way to generate knowledge from the propositions reflecting facts or directly from data We intend to extract new knowledge in the form of definitions given as fixed point equations. An appropriate fixed point theory is outlined in favour of our aim. This theory suggests the so called generative fixed point equatio...

A logic procedure is provided as to discover relations inductively from experimental data. This logic inductive inference method discovers the properties of the relations in question step by step in the form of fixed point equations.
The defining formulas in these equations may use only bounded quantifiers but the relation to be defined may also ne...

Simulation modeling is an essential part of solving problems related to the analysis and/or synthesis of objects of high complexity. The conceptual frame of model building presented here considers the objects in question as a goal oriented system consisting of knowledge, set of actions, scale of values, set of goals and time parameters. Moreover, e...

In the article the use of mathematical logic for system simulation is introduced.

The problems of the solver of the “plausible inference + deduction” type development are considered in the paper.

A methodological frame is presented allowing both appropriate characterization of expert systems and their development. This frame is based on the theory of intelligent actors which contains strictly formal tools together with the basic concepts of activity theory from cognitive psychology. First the activity model of problem solving is discussed i...

Cooperative problem solving is concerned where intelligent actors are organized into a unique system to understand and solve the given problem. The approach followed here is based on the theory of activity from cognitive psychology and also on a parallel computation model. An appropriate descriptive language is given based on logic simulation (TS-P...

A modified version of PHR~- resolution comprising negative hyper-resolution and paramodulation is introduced to reduce the search of statements that contain transi tive relations. Let R be a symbol of transitive relation and let a nucleus contain the literal tRp, and let a factor of an elec tron be of the form C V nt,Rt 2 .Moreover let us suppose...

The center of study is programming that allows communication between program and its environment. A modified version of Hoare's CSP is applied as programming language and its main features in connection with semantics and completeness are investigated. Semantics is based on an appropriate type of games by using its tree representation. These entiti...

Computer simulation plays an important role within the solution of those problems which are connected with analysis or synthesis of objects of high complexity. The main characteristics of simulation models and their development are analysed.
In order to support the development a consistent family of formal notions are briefly introduced within the...

## Projects

Projects (4)

The REACTION project develops an integrated approach to improve long term management of diabetes, continuous blood glucose monitoring, clinical monitoring and intervention strategies, monitoring and predicting related disease indicators, complemented by education on life style factors such as obesity and exercise and, ultimately, automated closed-loop delivery of insulin.

The project goal is creation of symbiotic man-computer complex