A System for Deduction-based Formal Verification of Workflow-oriented Software Models

The work concerns formal verification of workflow-oriented software models using deductive approach. The formal correctness of a model's behaviour is considered. Manually building logical specifications, which are considered as a set of temporal logic formulas, seems to be the significant obstacle for an inexperienced user when applying the deductive approach. A system, and its architecture, for the deduction-based verification of workflow-oriented models is proposed. The process of inference is based on the semantic tableaux method which has some advantages when compared to traditional deduction strategies. The algorithm for an automatic generation of logical specifications is proposed. The generation procedure is based on the predefined workflow patterns for BPMN, which is a standard and dominant notation for the modeling of business processes. The main idea for the approach is to consider patterns, defined in terms of temporal logic,as a kind of (logical) primitives which enable the transformation of models to temporal logic formulas constituting a logical specification. Automation of the generation process is crucial for bridging the gap between intuitiveness of the deductive reasoning and the difficulty of its practical application in the case when logical specifications are built manually. This approach has gone some way towards supporting, hopefully enhancing our understanding of, the deduction-based formal verification of workflow-oriented models.Comment: International Journal of Applied Mathematics and Computer Scienc

Learning Deductive Reasoning from Synthetic Corpus based on Formal Logic

We study a synthetic corpus-based approach for language models (LMs) to acquire logical deductive reasoning ability. The previous studies generated deduction examples using specific sets of deduction rules. However, these rules were limited or otherwise arbitrary. This can limit the generalizability of acquired deductive reasoning ability. We rethink this and adopt a well-grounded set of deduction rules based on formal logic theory, which can derive any other deduction rules when combined in a multistep way. We empirically verify that LMs trained on the proposed corpora, which we name $\textbf{FLD}$ ($\textbf{F}$ormal $\textbf{L}$ogic $\textbf{D}$eduction), acquire more generalizable deductive reasoning ability. Furthermore, we identify the aspects of deductive reasoning ability on which deduction corpora can enhance LMs and those on which they cannot. Finally, on the basis of these results, we discuss the future directions for applying deduction corpora or other approaches for each aspect. We release the code, data, and models

Semantics of Deductive Databases in a Membrane Computing Connectionist Model

The integration of symbolic reasoning systems based on logic and connectionist systems based on the functioning of living neurons is a vivid research area in computer science. In the literature, one can found many e orts where di erent reasoning systems based on di erent logics are linked to classic arti cial neural networks. In this paper, we study the relation between the semantics of reasoning systems based on propositional logic and the connectionist model in the framework of membrane computing, namely, spiking neural P systems. We prove that the xed point semantics of deductive databases and the immediate consequence operator can be implemented in the spiking neural P systems model

Semantics of Deductive Databases in a Membrane Computing Connectionist Model

The integration of symbolic reasoning systems based on logic and connectionist systems based on the functioning of living neurons is a vivid research area in computer science. In the literature, one can found many e orts where di erent reasoning systems based on di erent logics are linked to classic arti cial neural networks. In this paper, we study the relation between the semantics of reasoning systems based on propositional logic and the connectionist model in the framework of membrane computing, namely, spiking neural P systems. We prove that the xed point semantics of deductive databases and the immediate consequence operator can be implemented in the spiking neural P systems model

Integration of Similarity-based and Deductive Reasoning forKnowledge Management

Many disciplines in computer science combine similarity-based and logic-based reasoning. The problem is that the disciplines combine these independently of each other. For example in Case-Based Reasoning (CBR) (Aamodt and Plaza, AI Commun. 7(1):39-59, 1994; Bergmann etal., Künstl. Intell. 23(1):5-11, 2009; Bergmann, Experience Management: Foundation, Development, Methodology and Internet-based Applications, LNAI, vol.2432, Springer, Berlin, 2002), the combination is applied in a sequential manner and not systematically as follows: a set of solutions is retrieved from a case-base using a similarity measure and then deductive reasoning is applied to adapt the retrieved solutions to a query. The aim of this dissertation (Mougouie, Ph.D. thesis, Trier University, Germany, 2009) is to integrate similarity-based and deductive reasoning in a unified manner within the context of Knowledge Management (KM

EXPLORATION THE STUDENTS REASONING IN SOLVING TRIGONOMETRY PROBLEMS IN TERMS OF THE ABILITY OF LOGICAL THINKING

Reasoning has been researched by many experts. However, the research of students in reasoning in solving Trigonometry is not sufficient. This research is a qualitative research used to explore students' reasoning in Trigonometry based on logical ability and comparation between subjects with high-logic ability and subjects with medium-logic ability. The instruments in this research are the researchers themselves as the main instrument guided by math-problems solving task and valid and reliable interview manual. The data collection is done by task-based interview. The subjects of the research is the XII-IPA students which consists of 2 people. The research process follows these stages : (a) formulate the reasoning indicators in solving math problems based on relevant theory and research, (b) formulate valid and reliable supporting instruments (math problems solving task and interview manual), (c) collecting the research subject by giving logical ability test, (d) data collecting to reveal students' reasoning in solving math problems, (e) conclude the research result. The result shows: (1) the similar method between the high-logic subject and the medium-logic subject is in solving each Trigonometry question, they always start with inductive reasoning and then continue with deductive reasoning, (2) the difference between the subjects reasoning of high-logic ability and medium-logic ability was on the process of reasoning between two those two subjects on each of problem solving according to Polya’s steps. Based on the result, the students' reasoning can be a reference in developing math learning model to improve students reasoning abilty base on logical thinking. Keyword : Mathematics Reasoning, Logical Thinkin

The Founding of Logic: Modern Interpretations of Aristotle’s Logic

Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the epistemic process of extracting information implicit in explicitly given information) and, second, the process of establishing knowledge that a conclusion does not follow. Despite the overwhelming tendency to interpret the syllogistic as formal epistemology, it was not until the early 1970s that it occurred to anyone to think that Aristotle may have developed a theory of deductive reasoning with a well worked-out system of deductions comparable in rigor and precision with systems such as propositional logic or equational logic familiar from mathematical logic. When modern logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle's contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotle from possible charges of psychologism. They thought they saw Aristotle applying the informal axiomatic method to formal ontology, not as making the first steps into formal epistemology. They did not notice Aristotle's description of deductive reasoning. Ironically, the formal axiomatic method (in which one explicitly presents not merely the substantive axioms but also the deductive processes used to derive theorems from the axioms) is incipient in Aristotle's presentation. Partly in opposition to the axiomatic, ontically-oriented approach to Aristotle's logic and partly as a result of attempting to increase the degree of fit between interpretation and text, logicians in the 1970s working independently came to remarkably similar conclusions to the effect that Aristotle indeed had produced the first system of formal deductions. They concluded that Aristotle had analyzed the process of deduction and that his achievement included a semantically complete system of natural deductions including both direct and indirect deductions. Where the interpretations of the 1920s and 1930s attribute to Aristotle a system of propositions organized deductively, the interpretations of the 1970s attribute to Aristotle a system of deductions, or extended deductive discourses, organized epistemically. The logicians of the 1920s and 1930s take Aristotle to be deducing laws of logic from axiomatic origins; the logicians of the 1970s take Aristotle to be describing the process of deduction and in particular to be describing deductions themselves, both those deductions that are proofs based on axiomatic premises and those deductions that, though deductively cogent, do not establish the truth of the conclusion but only that the conclusion is implied by the premise-set. Thus, two very different and opposed interpretations had emerged, interestingly both products of modern logicians equipped with the theoretical apparatus of mathematical logic. The issue at stake between these two interpretations is the historical question of Aristotle's place in the history of logic and of his orientation in philosophy of logic. This paper affirms Aristotle's place as the founder of logic taken as formal epistemology, including the study of deductive reasoning. A by-product of this study of Aristotle's accomplishments in logic is a clarification of a distinction implicit in discourses among logicians--that between logic as formal ontology and logic as formal epistemology