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Design by Constract (DBC) has influenced the development of formal specification languages that allow the mix of specification and implementation code, like Eiffel, the Java Modeling Language (JML) and Spec#. Meanwhile algebraic... more
Design by Constract (DBC) has influenced the development of formal specification languages that allow the mix of specification and implementation code, like Eiffel, the Java Modeling Language (JML) and Spec#. Meanwhile algebraic specification languages have been developing independently and offer full support for specification and verification of design for large and complex systems in a mathematical rigorous way. However there is no guarantee that the final implementation will comply to the specification. In this paper we proposed the use of the latter for the specification and verification of the systems design and then by presenting a translation between the two, the use of the former to ensure that the implementation respects the specification and thus enjoy the verified properties.
ABSTRACT
In this paper, we suggest the broader concept of proof-event, introduced by Joseph Goguen, as a fundamental methodological tool for studying proofs in history of mathematics. In this framework, proof is understood not as a purely... more
In this paper, we suggest the broader concept of proof-event, introduced by Joseph Goguen, as a fundamental methodological tool for studying proofs in history of mathematics. In this framework, proof is understood not as a purely syntactic object, but as a social process that involves at least two agents; this highlights the communicational aspect of proving. We claim that historians of mathematics essentially study proof-events in their research, since the mathematical proofs they face in the extant sources involve many informal components, often not completely formalizable, and convey some kind of semantic content calling for understanding and verification. We illustrate the application of this methodological approach in some outstanding historical cases, paying particular attention to the process of proof interpretation that makes a proof-event alive. Finally, we suggest a classification of proof-events, according to the conditions imposed upon problem solving. This enables us to...
Research Interests:
Research Interests:
The protection of the distribution of digital contents via mobile networks has been standardized by Open Mobile Alliance (OMA) with the proposition of the OMA Digital Rights Management System. When multiple licenses refer to the same... more
The protection of the distribution of digital contents via mobile networks has been standardized by Open Mobile Alliance (OMA) with the proposition of the OMA Digital Rights Management System. When multiple licenses refer to the same content a decision ...
This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting-point is the concept of proof-event or proving,... more
This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting-point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts, in which problem-solving procedures and strategies are studied. We represent proof-events as problem-centered spatio-temporal processes by means of the language of the calculus of events, which captures adequately certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a " loose " semantics for the proof-events, by means of Kolmogorov's calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving.
Abstract Syntax Notation One (ASN. 1) is a very popular specification language with many applications in networking. We work towards the correct translation from ASN. 1, into the powerful algebraic specification language CafeOBJ. Our aim... more
Abstract Syntax Notation One (ASN. 1) is a very popular specification language with many applications in networking. We work towards the correct translation from ASN. 1, into the powerful algebraic specification language CafeOBJ. Our aim is to create a software ...
The new programming language Java carries object-orientation to extremes, treating all user-defined types as objects. We argue that this causes problems with readability, which we illustrate with examples. Java could have avoided these... more
The new programming language Java carries object-orientation to extremes, treating all user-defined types as objects. We argue that this causes problems with readability, which we illustrate with examples. Java could have avoided these problems if it had gonstructs for modules and for non-object data-types.
Research Interests:
Information Systems used in Education must take into account educational as well as technical aspects. Using educational information systems we must choose a balanced approach where: social, educational and technical aspects must... more
Information Systems used in Education must take into account educational as well as technical aspects. Using educational information systems we must choose a balanced approach where: social, educational and technical aspects must participate in the "right mix", so that to meet the set requirement of the system in the prospect of having a positive summative evaluation.
Research Interests:
Virtual career guidance - using distance education methods - can provide an educationally efficient and economically feasible way to support both students and counselors in the mutual interwoven role, thus improving the quality of... more
Virtual career guidance - using distance education methods - can provide an educationally efficient and economically feasible way to support both students and counselors in the mutual interwoven role, thus improving the quality of careers' guidance provision. In this paper, we present a comprehensive account on educational and occupational issues pertinent to our "information technology era" and stress on the usefulness, for each student to be informed and exploit the virtual career guidance techniques, in preparing better his/her professional "route".
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Institutions give an algebraic answer to the question what is a logic?. In our paper we inter- nalise "possible worlds semantics" and modal satisfaction to institutions with open formulæ (called open institutions) and fullfiling certain... more
Institutions give an algebraic answer to the question what is a logic?. In our paper we inter- nalise "possible worlds semantics" and modal satisfaction to institutions with open formulæ (called open institutions) and fullfiling certain mild technical conditions. Modalities then can be defined on "top" of any such institution proving that modal extensions are not a privilege of certain logics - like the first order one - but can be generated over a much wider variety of institutions.
Research Interests:
Our work extends CafeOBJ algebraic specification language to capture mobility. It uses the behavioral specification of hidden objects together with the concurrent object composition. This paper presents a CafeOBJ approach to location, one... more
Our work extends CafeOBJ algebraic specification language to capture mobility. It uses the behavioral specification of hidden objects together with the concurrent object composition. This paper presents a CafeOBJ approach to location, one of the two main entities of any mobile system (the other is the mobile object). We also present the equational specification of a control center.
Research Interests:
We define abstract
modal semantics using
institutions. Modalities
can then be generated
over a wide variety of
logics. Using tools
from institution-independent model
theory we state a
preservation result
for the modal satisfaction
Research Interests:
Our work extends CafeOBJ algebraic specification language to capture mobility. It uses the behavioral specification of hidden objects together with the concurrent object composition. This paper presents a CafeOBJ approach to location, one... more
Our work extends CafeOBJ algebraic specification language to capture mobility. It uses the behavioral specification of hidden objects together with the concurrent object composition. This paper presents a CafeOBJ approach to location, one of the two main entities of any mobile system (the other is the mobile object). We also present the equational specification of a control center.
Research Interests:
We present how to model real time authentication protocols with CafeOBJ algebraic specification language [1]. The protocols are specified as Timed Observational Transition Systems or TOTSs [2]. Based on this specification, we can... more
We present how to model real time
authentication protocols with CafeOBJ algebraic
specification language [1]. The protocols are
specified as Timed Observational Transition
Systems or TOTSs [2]. Based on this
specification, we can verify desirable properties
of the protocols through induction and/or case
analysis, thanks to the CafeOBJ system and its
support to the interactive theorem proving. The
method we apply is a combination of [2] and
[3]. As a case study we model TESLA protocol
[4], which is used for
the source authentication
in multicast communication settings, and verify
a safety property.
Research Interests:
Algebraic specification languages are formal methods that provide a rigorous basis for modeling of several systems. Security protocols are safety critical systems that need to be verified before their implementation. In this paper we have... more
Algebraic specification languages are formal methods that provide a rigorous basis for modeling of several systems. Security protocols are safety critical systems that need to be verified before their implementation. In this paper we have formally specified sensor network encryption protocol (SNEP) and a key agreement protocol for sensor networks, both from the SPINS protocol suite, with the OTS/CafeOBJ method, a well known formal specification technique applied not only in research, but also in industry. Based on this specification, we have proved that each protocol possesses an important safety(invariant) property.
Research Interests:
The adoption of algebraic specification techniques by the networks' research community is happening slowly but steadily. We present a software environment that can translate a protocol's specification, from Abstract Syntax Notation One... more
The adoption of algebraic specification techniques by the networks' research community is happening slowly but steadily. We present a software environment that can translate a protocol's specification, from Abstract Syntax Notation One (ASN.1), into the powerful algebraic specification language CafeOBJ. The resulting code can be used to check critical properties of systems. In this paper, we sketch some first steps towards the implementation of such a tool including a case study
Research Interests:
OMA-Digital Rights Management System is a standard proposed by Open Mobile Alliance for protecting digital content distributed through mobile networks. In such a system, licenses are written in an appropriate language and used to ensure... more
OMA-Digital Rights Management System is a standard proposed by Open Mobile Alliance for protecting digital content distributed through mobile networks. In such a system, licenses are written in an appropriate language and used to ensure the fine grained consumption of contents. We claim that the Rights Expression Language (OMA-REL) does not rely on formal semantics. To address this problem we propose an abstract syntax for OMA-REL and write an algebraic specification of it using CafeOBJ, an executable algebraic specification language, with the future goal the creation of automated tools that check the behavior of a set of licenses under a certain environment.
Research Interests:
The MPEG-2 encoding algorithm is a compression tool for moving pictures and associated audio, developed by the Moving Picture Experts Group (MPEG) and is designed to cover a wide range of requirements from “VHS quality” to“HDTV”. The... more
The MPEG-2 encoding algorithm is a compression tool for moving pictures and associated audio, developed by the Moving Picture Experts Group (MPEG) and is designed to cover a wide range of requirements from “VHS quality” to“HDTV”. The compression methods used by MPEG-2 are considered to be asymmetrical in the meaning that the encoder is more complex than the decoder. This approach is new because MPEG does not specify the whole encoding process. In fact, the most important step of the encoding algorithm (namely the algorithms used to produce the motion vector) is not specified. Only some basic steps and the format of the compatible output are explicit specified, so that each encoder provider can create his own interpretation of the algorithm. This technique has the benefit that the decoders will remain compatible even as the encoders evolve. Due to its high acceptance and wide use, it is important to verify that the algorithm works as expected using formal methods, not only testing. To this end, we have used CafeOBJ, an executable algebraic specification language, to specify the algorithm and prove some desirable safety properties. More precisely, we specified the MPEG-2 encoding algorithm, considering the unspecified by MPEG steps as black boxes, as an Observational Transition System in CafeOBJ, and created a formal proof that for any input the output is as expected, thus proving that the algorithm works correctly
Research Interests:
Nowadays more than ever, computer ethics and information law are particularly conducive to everyday applications. Stemming from this reality computer supported computer ethics is a promising area for research. Still, the complexity of... more
Nowadays more than ever, computer ethics and information law are particularly conducive to everyday applications. Stemming from this reality computer supported computer ethics is a promising area for research. Still, the complexity of issues involved and the different problems addressed on each individual occasion make this task a hard one. Formal methods is an area in computer science, which uses mathematics for the specification, design and verification of software and hardware systems. Usually, each formal method has its own semantics and depends on a particular logical system. Z, OBJ, VDM, CASL, B-Method, Petri Nets are few of the most well known formal methods. Most of the formal methods can be implemented in a computer. The advantage of using such methods is that they guarantee higher levels of correctness. In computer supported computer ethics, formal methods can be used to provide a report on where inconsistencies lie. For verification ([5]), the input may be a specification and a desired ethical property of a system, and the output may be either “Yes, the property is valid” or “The property is not valid”. Formal methodologies based on deontic logic provide a description and informal analysis of the commonalities in ethical discourse. For example, the logic model (DEAL) makes use of recent research in deontic, epistemic and action logic, and indicate - drawing on recent research in computer implementations of modal logic - how information systems that implement the proposed formalization may be developed [4]. Another interesting example is [2] (and [1]) where mechanized multi-agent deontic logics are considered as the appropriate vehicle for engineering trustworthy robots. Mechanically checked proofs in such logics can serve to establish the permissibility (or obligatoriness) of agent actions, and such proofs, when translated into English, can also explain the rationale behind those actions. As formal method they use the theorem prover Athena in order to encode a natural deduction system for a deontic logic. In our proposed paper, in addition to an overview, we will present a general framework for the formal methodologies of the computer supported computer ethics. This is based on the theory of institutions [3], an abstract model theoretic version of Tarki’s theory of truth. Without going into mathematical details we will describe the basic methodological principles and its potential applications. We claim that our approach can be combined with other approaches, as [7], thus providing new light into the promising relation among formal methods and computer ethics.
Research Interests:
MPEG-2 is a wide used group of standards, established by the Moving Picture Experts Group (MPEG), for the digital compression of broadcast-quality full-motion video. Due to its high acceptance, it is very important to ensure that it... more
MPEG-2 is a wide used group of standards, established by the Moving Picture Experts Group (MPEG), for the digital compression of broadcast-quality full-motion video. Due to its high acceptance, it is very important to ensure that it behaves in a correct manner. To avoid vulnerability problems the MPEG-2 encoding algorithm has been already formally specified and verified for its correctness. In this paper, we propose the use of the OTS/CafeOBJ Method in order to prove that two MPEG-2 encoding algorithms for the same input produce the same output. Our approach is based on a simplified parallel version of the MPEG-2 encoder. Also, we have proved a mutual exclusion property for this parallel algorithm.
Research Interests:
OMA-Digital Rights Management System is a standard proposed by the Open Mobile Alliance (OMA) for protecting digital content distribution via mobile networks. To solve the decision problem, in the case that multiple licenses refer to the... more
OMA-Digital Rights Management System is a standard proposed by the Open Mobile Alliance (OMA) for protecting digital content distribution via mobile networks. To solve the decision problem, in the case that multiple licenses refer to the same content, OMA suggests a license choice algorithm. This algorithm ensures the fine grained consumption of contents. CafeOBJ is a new generation algebraic specification language. We apply the OTS/CafeOBJ method to formally model, specify and verify the above mentioned license choice algorithm. More specifically, we develop the mathematical model of the OMA decision algorithm as an OTS, a kind of transition system expressed in an equational CafeOBJ specification style. Finally, we verify that this algorithm fulfills the following safety property: Whenever a license is chosen for a given content, then the license is valid at that specific time.
Research Interests:
Open governance is a political ideology which promotes the application of the open source and open content to the every-day practices of democratic governance. An example is legislation that is open to the general public: this openness... more
Open governance is a political ideology which promotes the application of the open source and open content to the every-day practices of democratic governance. An example is legislation that is open to the general public: this openness allows citizens to express their views on the government directly and in large numbers, and the collection of their opinions benefits policy and those who implement it, the law makers, because they can base their decision-making on a wide range of tangible and specific data. These views, moreover, can suggest many different approaches of how open governance can merge with actual government. A most crucial factor though concerns how to succeed processing the vast amount of information within an open source environment.

Few days after the Greek parliamentary elections of the 4th of October of 2009 the newly elected socialist government launched the Greek OpenGov.gr initiative. The idea was to render OpenGov.gr a major reference point to Greek public sphere, a “virtual” meeting point of the government and the citizens. Some early initiatives included open calls for the filling of governmental posts and for participation in commentary forums formed in order to discuss and deliberate online over proposed legislation. It received major publicity since it was the first time in Greece that software tools and the Internet were openly offered to the public at a large scale to interact directly with the government. In a society that only 18,3% of its citizens have advanced or good Internet skills this initiative generated remarkable media attention. This led to an unexpectedly large civic participation: applications for certain positions or comments on legislation sometimes numbered several thousand. An interesting similar initiative is Labs.OpenGov.gr. This is an open innovation contest for the redesign of electronic government services. The response from the citizens was remarkable and the 15 best proposals that received top ranking are under consideration for adoption by the Greek e-state. The socialist party now in government has long being engaged in a number of similar projects while still in opposition.

In our paper we are going to present the political and technical impact the OpenGov.gr initiative has had so far, by exposing the considerable interest this initiative generated as this interest was recorded in the media, electronic and print, and an assortment of political information sources. It is obvious that OpenGov.gr is a top-down approach to open e-government. We are going to present its dynamic capabilities using stage models for transformation as a key potential accelerator for political change of the Greek governance. Also, we are going to present the impact that such initiatives may have to fight corruption and compare it with other countries.
Research Interests:
Sensor Network Encryption Protocol (SNEP) is one of the secure building blocks of the SPINS Protocol Suite and provides data confidentiality, two-party data authentication and evidence of data freshness in a wireless sensor network. We... more
Sensor Network Encryption Protocol (SNEP) is one of the secure building blocks of the SPINS Protocol Suite and provides data
confidentiality, two-party data authentication and evidence of data freshness in a wireless sensor network. We have formally
analyzed SNEP and a node-to-node key agreement protocol based on it, using the OTS/CafeOBJ method. Among other invariants,
we have verified that the protocols possess the important security properties of authenticity and confidentiality of relevant
message components. To our knowledge, we are the first to formally analyze SNEP using algebraic specification techniques.
Research Interests:
Digital Right Management (DRM) Systems have been created to meet the need for digital content protection and distribution. In this paper we present some of the directions of our ongoing research to apply algebraic specification techniques... more
Digital Right Management (DRM) Systems have been created to meet the need for digital content protection and distribution. In this paper we present some of the directions of our ongoing research to apply algebraic specification techniques on mobile DRM systems.
Research Interests:
Standards allow legal knowledge to become exploitable and can lead to fruitful data mining from Legal Departments and individuals. For example, in the Estrella project: using XML-standards [HBBB07], all the main elements of an LKIF... more
Standards allow legal knowledge to become exploitable and can lead to fruitful data mining from Legal
Departments and individuals.  For example,  in the Estrella project:  using XML-standards [HBBB07],
all the main elements of an LKIF document may allow them to be referenced in other legal documents,
anywhere on the World Wide Web.
Legal  Documents  can  be  de
ned  as  formal  theories  over  a  speci
c  logic.  Formal  features  of  a  Legal
Document Management System (LDMS) should include versioning, metadata, security, as well as index-
ing and retrieval.  Formal methodologies involve also stages such as formal speci
cation and veri
cation
[Ste11].  We claim that the lifecycle of legal documents can be seen as a fruitful domain of applications
for both the above stages.
In our paper, we will advance on the theoretical point why such an organization of legal documents will
improve transparency, trust and will accelerate the award of justice.  We propose that the enrichment of an LDMS with specification and verification techniques stimulates the ground for many applications of information law, including areas such as IP rights, Big Data and public procurement law
Research Interests:
Formal methods, while very promising, are being adopted by software/protocol engineers very slowly, as the industry has little motivation to move into this new, unknown territory. At the same time, new industrial standards are being... more
Formal methods, while very promising, are being adopted by software/protocol engineers very slowly, as the industry has little motivation to move into this new, unknown territory. At the same time, new industrial standards are being released quite frequently, as standardization seems to be very popular among developers. In this paper we present the idea of blending formal methods with industry standards. We claim that this results in more concrete system design and extended property verification tools. The enhancement of industry standards with formal methodologies leads to better understanding of the designed environment, eliminates ambiguity and forces a certain level of precision into the specification. An extra benefit is that we can use one of the many algebraic specification languages in order to assist with property checking/verification.
Research Interests:
While collaboration has always played an important role in many cases of discovery and creation, recent developments such as the web facilitate and encour-age collaboration at scales never seen before, even in areas such as mathematics,... more
While collaboration has always played an important role in many cases of discovery and creation, recent developments such as the web facilitate and encour-age collaboration at scales never seen before, even in areas such as mathematics, where contributions by single individuals have historically been the norm. This new scenario poses a challenge at the theoretical level, as it brings out the importance of various issues which, as of yet, have not been sufficiently central to the study of problem-solving, discovery, and creativity. We analyze the case of collective and web-based proof-events in mathematics, which share their temporal and social na-ture with every case of collective problem-solving. We propose that some ideas from cognitive architectures, in particular the notion of codelet — understood as an agent engaged in one of a multitude of available tasks — can illuminate our un-derstanding of collective problem-solving, and act as a natural bridge from some of the theoretical aspects of collective, web-based discovery to the practical concern of designing cognitively-inspired systems to support collective problem-solving. We use the Pythagorean Theorem and its many proofs as a case study to illustrate our approach.
Research Interests:
With the help of the Internet, social networks have grown rapidly. This has increased security requirements. We present a formalization of social networks as composite behavioral objects, defined using the Observational Transition System... more
With the help of the Internet, social networks have grown rapidly. This has increased security requirements. We present a formalization of social networks as composite behavioral objects, defined using the Observational Transition System (OTS) approach. Our definition is then translated to the OTS/CafeOBJ algebraic specification methodology. This translation allows the formal verification of safety properties for social networks via the Proof Score method. Finally, using this methodology we formally verify some security properties.
Research Interests:
The vigorous impact of the Web in time and space arises from the fact that it motivates massive creation, editing and distribution of information by Users with little knowledge. This unprecedented continuum provides novel opportunities... more
The vigorous impact of the Web in time and space arises from the fact that it motivates massive creation, editing and distribution of information by Users with little knowledge. This unprecedented continuum provides novel opportunities for innovation but also puts under jeopardy its survival as a stable construct that nurtures a complex system of connections. We examine the Web as an ethics determined space by demonstrating Hayek's theory of freedom in a three-leveled Web: technological, contextualized and economic. Our approach accounts for the co-dependence of code and values, and assumes that the Web is a self-contained system that exists in and by itself. This view of internal Web ethics directly connects the concept of freedom with issues like centralization of traffic and data control, rights on visiting log file, custom User profiles and the interplay among function, structure and morality of the Web. It is also demonstrated, in the case of Net Neutrality, that generic freedom-coercion trade-offs are incomplete in treating specific cases at work.
Research Interests:
We present an abstract model of the Semantic Web stack, using algebraic specifications. This work is a first step towards a unifying framework for the various Semantic Web technologies that will allow reasoning tasks to be performed, via... more
We present an abstract model of the Semantic Web stack, using algebraic specifications. This work is a first step towards a unifying framework for the various Semantic Web technologies that will allow reasoning tasks to be performed, via rewriting and behavioral logic.
Research Interests:
Service oriented architectures and event driven enviroments are becoming dominant over the web. Reactive Rules expressed by Rule Markup Languages are used to define the system’s reactions. In this paper we present a Hidden (Sorted)... more
Service oriented architectures and event driven enviroments are becoming dominant over the web. Reactive Rules expressed by Rule Markup Languages are used to define the system’s reactions. In this paper we present a Hidden (Sorted) Algebra approach to some of the most common families of Reactive Rules. This semantics will allow the mapping between Rule Markup Languages and Behavioral Algebraic Specification Languages. Verification techniques for reactive rules, will provide automated reasoning capabilities and support the development of new rule based policies and trust models.
Research Interests:
The Timed Observational Transition System (TOTS)/CafeOBJ method is a version of the OTS/CafeOBJ method for modeling, specification and verification of distributed systems and protocols with real time constraints. In this paper we report... more
The Timed Observational Transition System (TOTS)/CafeOBJ method is a version of the OTS/CafeOBJ method for modeling, specification and verification of distributed systems and protocols with real time constraints. In this paper we report on a case study from the field of source authentication protocols, TESLA protocol, to show the application of the method to such complex systems. We prove that our model of the protocol satisfies that the receiver does not accept as authentic any message unless it was actually sent by the sender. To verify the property we have used several other invariants which include timing information. To our knowledge, this is the first time that the method has been applied to the formal analysis of such a complex protocol.
Research Interests:
Research in the field of computational media is gaining momentum as it explores the expressive potential of generative art. Our project seeks to build on previous work done in this area, exploring the creative possibilities of a hybrid... more
Research in the field of computational media is gaining momentum as it explores the expressive potential of generative art. Our project seeks to build on previous work done in this area, exploring the creative possibilities of a hybrid form of new media and its potential as a powerful new expressive tool which can lead to meaningful insights into the creative process and how we perceive.
Research Interests:
We claim that a new relation can be developed between the well-known theory of institutions and semantic networks. In particular, we argue that the many different types of semantic networks that have been used in the field of applied... more
We claim that a new relation can be developed between the well-known theory of institutions and semantic networks. In particular, we argue that the many different types of semantic networks that have been used in the field of applied computer science can be formalized mathematically using the theory of institutions. We demonstrate the first steps towards such an institution-based theory of semantic networks, using the familiar proof that first-order logic is an institution to provide an indicative such framework.
Research Interests:

And 47 more

"Goguen proposed the concept of proof-event to signify a new approach to proof, designed to cover apodictic, dialectical, constructive, non-constructive proof, as well as proof steps and computer proofs. Proof-events are spatio-temporal... more
"Goguen proposed the concept of proof-event to signify a new approach to proof, designed to cover apodictic, dialectical, constructive, non-constructive proof, as well as proof steps and computer proofs. Proof-events are spatio-temporal social processes that necessarily require two agents: a prover and an interpreter for their understanding and final validation. They allow any semiotic system as a means of formulation and communication and incorporate the history of proof.
Proof events generate proofs presented in different styles, which characterize different cultures, schools or scholars that may differ in views of meta-theoretical character. Style can be defined as a meta-code that determines the individual mode of integration (selection, combination, blending) of concepts into a narrative structure (proof). Style then depends on the underlying mode of signification (semiosis), the selected code and the underlying conceptual space."