Strategic Issues, Problems and Challenges in Inductive Theorem Proving

Abstract(Automated) Inductive Theorem Proving (ITP) is a challenging field in automated reasoning and theorem proving. Typically, (Automated) Theorem Proving (TP) refers to methods, techniques and tools for automatically proving general (most often first-order) theorems. Nowadays, the field of TP has reached a certain degree of maturity and powerful TP systems are widely available and used. The situation with ITP is strikingly different, in the sense that proving inductive theorems in an essentially automatic way still is a very challenging task, even for the most advanced existing ITP systems. Both in general TP and in ITP, strategies for guiding the proof search process are of fundamental importance, in automated as well as in interactive or mixed settings. In the paper we will analyze and discuss the most important strategic and proof search issues in ITP, compare ITP with TP, and argue why ITP is in a sense much more challenging. More generally, we will systematically isolate, investigate and classify the main problems and challenges in ITP w.r.t. automation, on different levels and from different points of views. Finally, based on this analysis we will present some theses about the state of the art in the field, possible criteria for what could be considered as substantial progress, and promising lines of research for the future, towards (more) automated ITP

Requirements modelling and formal analysis using graph operations

The increasing complexity of enterprise systems requires a more advanced analysis of the representation of services expected than is currently possible. Consequently, the specification stage, which could be facilitated by formal verification, becomes very important to the system life-cycle. This paper presents a formal modelling approach, which may be used in order to better represent the reality of the system and to verify the awaited or existing system’s properties, taking into account the environmental characteristics. For that, we firstly propose a formalization process based upon properties specification, and secondly we use Conceptual Graphs operations to develop reasoning mechanisms of verifying requirements statements. The graphic visualization of these reasoning enables us to correctly capture the system specifications by making it easier to determine if desired properties hold. It is applied to the field of Enterprise modelling

Pengaruh Strategi Pembelajaran Induktif (Melalui Metode Ceramah dengan Metode Diskusi) dan Motivasi Belajar terhadap Pengetahuan Siswa Tentang Keanekaragaman Hayati Eksperimen di MTs Al Hikmah Pulogadung Jakarta

The objective of this research in the find out the effect of extension strategy Inductive (lecture method vs discussion method) and the learning motivation on the student’s knowledge about diversity. The strategy used was a quasi-experiment of 2 x 2 factorial design on the grade-VII students of Public Junior High School – Al-Hikmah Jakarta. The sample 0f 70 students were used, which they were divided in group. The results showed as follows; (1) there is a significant difference between the students knowledge about environment that was taught with lecture method with the students taught with the discussion method, (2) there is an interaction found between instructional inductive strategy and learning motivation on the student’s knowledge about diversity, (3) the students group that process high learning motivation, their knowledge about diversity  is higher with the problem solving strategy than with discussion method, and (4) the low level of learning motivation student’s, their knowledge about diversity is better by lecture method than the discussion method. From the research, the conclusion is that the lecture method can be effective to increase the level of the knowledge about diversity by consideration their learning motivation. Keywords: Knowledge about diversity, learning motivation, lecture method, extention inductive strateg

Récurrence noethérienne pour le raisonnement de premier ordre

National audienceLa récurrence nœthérienne est un des principes les plus généraux de raisonnement formel. Dans le cadre du raisonnement de premier ordre, nous présentons une classification de ses instances pouvant être partagées en instances basées sur des termes et des formules. Nous donnons un aperçu du raisonnement par récurrence nœthérienne basée sur des termes et sur des formules, puis nous établissons des relations entre eux. Enfin, nous présentons une méthodologie pour la certification du raisonnement basé sur des formules à l’aide de l’assistant de preuve Coq

Synthesising end-to-end security schemes through endorsement intermediaries

Composing secure interaction protocols dynamically for e-commerce continue to pose a number of challenges, such as lack of standard notations for expressing requirements and the difficulty involved in enforcing them. Furthermore, interaction with unknown entities may require finding common trusted intermediaries. Securing messages sent through such intermediaries require schemes that provide end-to-end security guarantees. In the past, e-commerce protocols such as SET were created to provide such end-to-end guarantees. However, such complex hand crafted protocols proved difficult to model check. This thesis addresses the end-to-end problems in an open dynamic setting where trust relationships evolve, and requirements of interacting entities change over time. Before interaction protocols can be synthesised, a number of research questions must be addressed. Firstly, to meet end-to-end security requirements, the security level along the message path must be made to reflect the requirements. Secondly, the type of endorsement intermediaries must reflect the message category. Thirdly, intermediaries must be made liable for their endorsements. This thesis proposes a number of solutions to address the research problems. End-to-end security requirements were arrived by aggregating security requirements of all interacting parties. These requirements were enforced by interleaving and composing basic schemes derived from challenge-response mechanisms. The institutional trust promoting mechanism devised allowed all vital data to be endorsed by authorised category specific intermediaries. Intermediaries were made accountable for their endorsements by being required to discharge or transfer proof obligations placed on them. The techniques devised for aggregating and enforcing security requirements allow dynamic creation of end-to-end security schemes. The novel interleaving technique devised allows creation of provably secure multiparty schemes for any number of recipients. The structured technique combining compositional approach with appropriate invariants and preconditions makes model checking of synthesised schemes unnecessary. The proposed framework combining endorsement trust with schemes making intermediaries accountable provides a way to alleviate distrust between previously unknown e-commerce entities

www.elsevier.com/locate/entcs Strategic Issues, Problems and Challenges in Inductive Theorem Proving

(Automated) Inductive Theorem Proving (ITP) is a challenging field in automated reasoning and theorem proving. Typically, (Automated) Theorem Proving (TP) refers to methods, techniques and tools for automatically proving general (most often first-order) theorems. Nowadays, the field of TP has reached a certain degree of maturity and powerful TP systems are widely available and used. The situation with ITP is strikingly different, in the sense that proving inductive theorems in an essentially automatic way still is a very challenging task, even for the most advanced existing ITP systems. Both in general TP and in ITP, strategies for guiding the proof search process are of fundamental importance, in automated as well as in interactive or mixed settings. In the paper we will analyze and discuss the most important strategic and proof search issues in ITP, compare ITP with TP, and argue why ITP is in a sense much more challenging. More generally, we will systematically isolate, investigate and classify the main problems and challenges in ITP w.r.t. automation, on different levels and from different points of views. Finally, based on this analysis we will present some theses about the state of the art in the field, possible criteria for what could be considered as substantial progress, and promising lines of research for the future, towards (more) automated ITP