The Database, Logic, and Suffering _Memento_ and Random-Access Information Aesthetic.

While logical theories of information attitudes, such as knowledge, certainty and belief, have flourished in the past two decades, formalization of other facets of rational behavior have lagged behind significantly. One intriguing line of research concerns the concept of intention. I will discuss one approach to tackling the notion within a logical framework, based on a database perspective.

We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of predicate calculus. Our algebraic framework unifies natural joins and data dependencies of database theory and relational algebra of clone theory with the bond algebra of C.S. Peirce. We also offer new constructions of reductions, systematically study irreducible relations and reductions to them and introduce a new characteristic (...) of relations, ternarity, that measures their ‘complexity of relating’ and allows to refine reduction results. In particular, we refine Peirce’s controversial reduction thesis, and show that reducibility behaviour is dramatically different on finite and infinite domains. (shrink)

This paper concerns the paraconsistent logic LPQ⊃,F and an application of it in the area of relational database theory. The notions of a relational database, a query applicable to a relational database, and a consistent answer to a query with respect to a possibly inconsistent relational database are considered from the perspective of this logic. This perspective enables among other things the definition of a consistent answer to a query with respect to a possibly (...) inconsistent database without resort to database repairs. In an earlier paper, LPQ⊃,F is presented with a sequent-style natural deduction proof system. In this paper, a sequent calculus proof system is presented instead because such proof systems are generally considered more suitable as the basis of proof search procedures than natural deduction proof systems and proof search procedures can serve as the core of algorithms for computing consistent answers to queries. (shrink)

"Database of medieval Latin Texts on logic and semantics in medieval manuscripts, founded on the card files of Professor em. L.M. de Rijk." Bulletin de Philosophie Médiévale, 40(), pp. 129–130.

ABSTRACT We introduce a two-dimensional temporal logic as a formalism which enables the description of both the history of a world and the evolution of an observer's views about the history. We apply such formalism to the description of certain problems that occur in historical database systems due to updates. The historical dimension describes the history of a world according to an observer's view at a certain moment in time. The transaction dimension describes the evolution of an observer's (...) view; changes can occur in the observer's view of the present and future as well as in his views of the past. The database is seens as an observer of the history of the world. Besides describing the history of the world, the database system can also execute temporal specifications in the form of temporal actions. The two-dimensional formalism is used to describe the effects of updates in the execution of temporal actions. The detection of some problematic effects and its implementation are discussed. (shrink)

This paper introduces and studies a declarative framework for updating views over indefinite databases. An indefinite database is a database with null values that are represented, following the standard database approach, by a single null constant. Typically a database is represented by a single set of facts |$D$| that model what is known to be true. This paper proposes a model of an indefinite extensional database that is more expressive with respect to the closed-world assumption (...) (CWA) adapted for the setting of indefinite databases (Libkin, 1995, A semantics-based approach to design of query languages for partial information. In Semantics in Databases, vol. 1358 of LNCS, pp. 170–208. Springer; der Meyden, 1998, Logical approaches to incomplete information: a survey. In Logics for Databases and Information Systems, pp. 307–356. Kluwer Academic Publishers, Norwell, MA, USA). More specifically, in our model, databases are determined by two sets of facts: |$D$| representing, as usual, all facts that are true in the database, and |$E$| that is meant to represent exceptions to the ‘unknown range’, i.e. facts that cannot be unknown. Intuitively, unless they are explicitly implied to be true by the first set, the facts specified as exceptions are assumed false. The semantics is given by means of a two-level CWA tailored to the case of indefinite information. The paper characterizes the semantics of indefinite databases in terms of their possible worlds that are obtained by instantiating occurrences of null values by concrete constants and defines several classes of database repairs that realize view-update requests. Most notable is the class of constrained repairs. Constrained repairs change the database ‘minimally’and avoid making arbitrary commitments. They narrow down the space of alternative ways to fulfill the view-update request to those that are grounded, in a certain strong sense, in the database, the view and the view-update request. (shrink)

In business and government, databases contain large quantities of digital transactional data (purchases made, services used, finances transferred, benefits received, licences acquired, borders crossed, tickets purchased). The data can be understood as ongoing and dynamic measurements of the activities and doings of people. In government, numerous database devices have been developed to connect such data across services to discover patterns and identify and evaluate the performance of individuals and populations. Under the UK’s New Labour government, the development of such (...) devices was part of a broader policy known as ‘joined-up thinking and government’. Analyses of this policy have typically understood joining up as an operation of adding together distributed data about subjects, which can then be used in the service of government surveillance, the database state or informational capitalism. But rather than such technical or managerialist analytics, I argue that topological analytics capture what these database devices enact and do: they materialize the ‘individuality’ of subjects in intensified, distributed and fluctuating ways and materialize and intensify a logic of what Deleuze describes as modulating controls. Through examples of UK New Labour social policy initiatives over the past decade, I argue that topological analytics can account for these as immanent rather than exceptional properties of database devices and, as such, part and parcel of a governmental logic and ontology of subjects. (shrink)

This paper describes an experimental platform for approximate knowledge databases called the Approximate Knowledge Database, based on a semantics inspired by rough sets. The implementation is based upon the use of a standard SQL database to store logical facts, augmented with several query interface layers implemented in JAVA through which extensional, intensional and local closed world nonmonotonic queries in the form of crisp or approximate logical formulas can be evaluated tractably. A graphical database design user interface is (...) also provided which simplifies the design of databases, the entering of data and the construction of queries. The theory and semantics for AKDBs is presented in addition to application examples and details concerning the database implementation. (shrink)

Generalized databases will be examined, in which attributes can be sets of attributes, or sets of sets of attributes, and other higher type constructs. A precise semantics will be developed for such databases, based on a higher type modal/intensional logic.

ABSTRACT To more efficiently cover a wide spectrum of conceptual modeling applications such as computer-aided design, computer-aided manufacturing, and medical information systems, we envision multi-paradigm design environments which have reasoning capability to support analyzing specifcations for correctness. For such applications, information system designers employ conceptual models characterized by semantically-rich specification languages. The problem of providing a comprehensive formal framework for such languages has not been adequately addressed. This paper investigates a formal system for this purpose called Event-Formula Logic (EFL). (...) The analysis focuses in particular on characterizing correctness of database updates. Its applicability is demonstrated from two perspectives: deriving preconditions that guarantee a given update will not violate an integrity constraint, and determining alternative integrity maintenance rules for performing corrective actions when the application semantics requires this update interpretation. The work described in this paper represents an important step in the analysis of database update semantics through the use of algorithmic logic. As a result, it contributes towards providing a formal basis for semantically-rich information system design environments. (shrink)

We extend the earlier results on the equivalence between the Boolean and the multivalued dependencies in relational databases and fragments of the Boolean propositional logic. It is shown that these equivalences are still valid for the databases that store complex data elements obtained from the recursive nesting of record, list, set and multiset constructors. The major proof argument utilises properties of Brouwerian algebras.The equivalences have several consequences. Firstly, they provide new insights into databases that are not in first normal (...) form. Secondly, they characterise the implication of data dependencies in nested databases in purely logical terms. The database designer can take advantage of these equivalences to reduce database design problems to well-studied problems in Boolean propositional logic. Furthermore, relational database design solutions can be reused to solve problems for nested databases. (shrink)

This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal Inconsistency (...) (LFI) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent first-order logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning. (shrink)

The paper discusses the potential value of a deontic approach to database specification. More specifically, some different types of integrity constraints are considered and a distinction is drawn between necessary (hard) and deontic (soft) constraints.Databases are compared with other normative systems. A deontic logic for database specification is proposed and the problems of how to react to, and of how to correct, or repair, a situation which arises through norm violation are discussed in the context of this (...) logic. The limitations of the proposed logic and possible modifications and extensions of it are analysed. (shrink)

This paper addresses the problem of querying several databases considered as a whole. Assuming that the different databases share a common data description language, the problem that arises is to consistently answer queries even if the database contents are contradictory. The main contribution of this paper is the specification of a query-evaluator for answering closed and open general queries addressed to several databases and for providing explanations about the results. For doing so, we first specify a query-evaluator, in (...) class='Hi'>logic, which assumes that the databases are propositional ones and do not contain disjunctions. Then we extend it to first-order databases defined by an extensional part and an intensional part. We also show that the query-evaluator corresponds to a majority merging of the databases. (shrink)

This paper explores the structural and epistemological role of databases within Specific Artificial Intelligence (SAI) systems designed for Artificial Research by Deduction. While traditional AI databases are primarily used for data storage, pattern recognition, and statistical analysis, the deductive paradigm demands a radically different architecture: databases must serve as axiomatic knowledge bases, containing formally defined propositions, inference rules, and logical constructs. In this context, the database is not merely passive storage but an active epistemic core from which provable knowledge (...) is derived. The paper proposes a framework for designing such databases to enable deductive reasoning engines to retrieve, manipulate, and verify knowledge systematically. Emphasis is placed on internal consistency, logical transparency, and the traceability of proofs. The study highlights how constructing these logic-oriented databases within SAI is a necessary precursor to scaling such capabilities within Global Artificial Intelligence (GAI), ensuring that artificial research remains coherent, explainable, and theoretically sound. (shrink)

This paper analyzes the similarities and differences between an ontology (focused on meaning), and a database schema (focused on data). We address questions about purpose, representation, creation, usage and semantics of each. We distill out twenty-five features that characterize these two representational artifacts, the majority of which are relevant to both. Each has a strong semantic heritage using formal logic to build conceptual models of some subject matter. And while there are differences in 90% of the features, the (...) differences are mostly historical, not technical. We identify pros and cons for each, and notice that there is usually no free lunch. The disadvantage that you think you are getting rid of may show up elsewhere in a different and unexpected way. We close by considering how ontology contributes to enterprise data integration. The emergence of using URIs as global identifiers (e.g. in OWL) dramatically enhances data integration as well as schema reuse and sharing. The primary focus on meaning helps ontology break through a lot of unnecessary complexity that exists in large traditional databases and greatly simplifies the process of integration. Ontology is providing a glimmer of light at the end of the tunnel for enterprise-wide data integration. (shrink)

We prove that the form of conditional independence at play in database theory and independence logic is reducible to the first-order dividing calculus in the theory of atomless Boolean algebras. This establishes interesting connections between independence in database theory and stochastic independence. As indeed, in light of the aforementioned reduction and recent work of Ben-Yaacov :957–1012, 2013), the former case of independence can be seen as the discrete version of the latter.

The Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and commonsense (...) reasoning, expert systems implementation, deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

1. Although the idea of measuring inconsistency was proposed in Grant (1978), the subject gained interest in 2002 with the publication of a proposal for measuring inconsistency in propositional kno...

Model organism databases are used extensively for knowledge retrieval and knowledge sharing among biologists. With the invention of genome sequencing and protein profiling technologies, large amount of molecular data provides practical insights into the molecular study of model organisms. The knowledge-intensive characteristic of model organism databases provides a reference point for the comparative study of other species. In this paper, I argue that algorithms could be used to facilitate cross-species research. I emphasize the epistemic significance of algorithms in the integration (...) of data for cross-species research. I examine (1) how algorithms guide data integration in model organism databases; and (2) the importance of algorithms for the use of model organism database in the cross-species research. I argue that an extrapolation from the stored data to other species is possible in virtue of the fact that algorithms can facilitate two modes of data integration—viz., inter-level and cross-species integration. Lastly, I examine the implication of the data integration role of an algorithm in light of mechanistic explanation. (shrink)

The language of logic can be used as a declarative programming language, i.e., the programmer has to describe what the problem is, not how it should be solved. We introduce logic programming by means of an example and explain how the system answers questions given a certain program. The possibility of recursive definitions is one of the cornerstones of logic programming. Prolog is a particular form of logic programming; it has been implemented in a certain way. (...) As a consequence, although declarative in principle, Prolog also has certain procedural aspects. The syntax of logic programming in general and of Prolog in particular is very simple. Although the reasoning mechanism should use unification, many systems work with a simpler form, called matching, for reasons of efficiency. Lists are important terms in logic programming. Cut is a procedural device needed to keep programs efficient. Negation is implemented by means of cut and hence differs from logical negation. Logic programming has many applications in (deductive) databases and in Artificial Intelligence. We discuss the most important pitfalls. (shrink)

Role-based database management systems are most widely used for information storage and analysis but are known as vulnerable to insider attacks. The core of intrusion detection lies in an adaptive system, where an insider attack can be judged if it is different from the predicted role by performing classification on the user’s queries accessing the database and comparing it with the authorized role. In order to handle the high similarity of user queries for misclassified roles, this paper proposes (...) a deep metric neural network with strategic sampling algorithm that properly extracts salient features and directly learns a quantitative measure of similarity. A strategic sampling method of heuristically generating and learning training pairs through Monte Carlo search is proposed to select a training pair that can represent the entire dataset. With the TPC-E–based benchmark data trained with 11,000 queries for 11 roles, the proposed model produces the classification accuracy of 95.41%, which is the highest compared with the previous models. The results are verified through comparison of quantitative and qualitative evaluations, and the feature space modelled in the neural network is analysed by t-SNE algorithm. (shrink)

Two things are done in this paper. First, a modal logic in which one can quantify over both objects and concepts is presented; a semantics and a tableau system are given. It is a natural modal logic, extending standard versions, and capable of addressing several well-known philosophical difficulties successfully. Second, this modal logic is used to introduce a rather different way of looking at relational databases. The idea is to treat records as possible worlds, record entries as (...) objects, and attributes as concepts, in the modal sense. This makes possible an intuitively satisfactory relational database theory. It can be extended, by the introduction of higher types, to deal with multiple-valued attributes and more complex things, though this is further than we take it here. (shrink)

The evaluative database provides efficient storage because it assumes defeasibly that values are additive, and hence the values of many compound features can be computed by summing the values of their constituents. This chapter completes the account by giving a precise characterization of the database calculation, investigating its logical credentials, and examining how it can be used for computing expected values. In the first section, the database calculation is formulated precisely. This is to treat it as a (...) principle for storing values in the evaluative database. In cases where values do not conform to the database calculation, they must be stored explicitly. For this to achieve compactness, it must be the case that values generally do conform to the database calculation. The second section shows that general principles of causal reasoning make it defeasibly reasonable to expect values to conform to the database calculation, thus justifying its use. (shrink)

In this paper, we argue that to apply rationality results of belief dynamics theory to various practical problems, it should be generalized in two respects: first of all, it should allow certain part of belief to be declared immutable; and secondly, the belief state need not be deductively closed. Such a generalization of belief dynamics, referred to as knowledge base dynamics, is presented, along with the concept of generalized contraction to contract a sentence from knowledge base. We show that knowledge (...) base dynamics has interesting connections with abduction, thus enabling us to use abductive procedures to realize contractions. Finally, we demonstrate how knowledge base dynamics can provide an axiomatic characterization for deleting view atoms from databases. (shrink)

The paper is devoted to applications of algebraic logic to databases. In databases a query is represented by a formula of first order logic. The same query can be associated with different formulas. Thus, a query is a class of equivalent formulae: equivalence here being similar to that in the transition to the Lindenbaum-Tarski algebra. An algebra of queries is identified with the corresponding algebra of logic. An algebra of replies to the queries is also associated with (...) algebraic logic. These relations lie at the core of the applications.In this paper it is shown how the theory of Halmos (polyadic) algebras (a notion introduced by Halmos as a tool in the algebraization of the first order predicate calculus) is used to create the algebraic model of a relational data base. The model allows us, in particular, to solve the problem of databases equivalence as well as develop a formal algebraic definition of a database's state description. In this paper we use the term "state description" for the logical description of the model. This description is based on the notion of filters in Halmos algebras. When speaking of a state description, we mean the description of a function which realizes the symbols of relations as real relations in the given system of data. (shrink)

Relational database management system is the most popular database system. It is important to maintain data security from information leakage and data corruption. RDBMS can be attacked by an outsider or an insider. It is difficult to detect an insider attack because its patterns are constantly changing and evolving. In this paper, we propose an adaptive database intrusion detection system that can be resistant to potential insider misuse using evolutionary reinforcement learning, which combines reinforcement learning and evolutionary (...) learning. The model consists of two neural networks, an evaluation network and an action network. The action network detects the intrusion, and the evaluation network provides feedback to the detection of the action network. Evolutionary learning is effective for dynamic patterns and atypical patterns, and reinforcement learning enables online learning. Experimental results show that the performance for detecting abnormal queries improves as the proposed model learns the intrusion adaptively using Transaction Processing performance Council-E scenario-based virtual query data. The proposed method achieves the highest performance at 94.86%, and we demonstrate the usefulness of the proposed method by performing 5-fold cross-validation. (shrink)

Databases play a fundamental role in today’s world, being used by most companies, especially those that offer services through the Internet. Today there is a wide variety of database models, each adapted for use according to the specific requirements of each application. Traditionally, the relational models with centralized architectures have been used mostly due to their simplicity and general-purpose query language, which made relational systems suitable for almost any application. However, with the growth of the Internet in recent decades, (...) both in the number of users and in the amount of information, those centralized models began to suffer availability and scalability issues. To address those issues, the use of decentralized architectures and alternative database models began to arise, eventually replacing relational databases and centralized architectures when the requirements on availability and scalability are high. Those database models alternative to the traditional relational model are grouped under the name of NoSQL. In this article, we present a NoSQL database developed as an end of degree work, with a flexible data model based on documents and a fully decentralized architecture based on the Gossip protocol for node discovery and a distributed hash table, in particular the rendezvous hashing algorithm, used to distribute and replicate the data across all the nodes. The main goals of the system are to achieve high availability and high scalability. High availability is achieved thanks to the replication of the data, while high scalability is achieved by its decentralized architecture, which allows multiple entry points from the requests, and the data distribution, effectively increasing the database capacity by increasing the number of nodes. (shrink)

The central hypothesis of the collaboration between Language and Computing (L&C) and the Institute for Formal Ontology and Medical Information Science (IFOMIS) is that the methodology and conceptual rigor of a philosophically inspired formal ontology greatly benefits application ontologies. To this end r®, L&C’s ontology, which is designed to integrate and reason across various external databases simultaneously, has been submitted to the conceptual demands of IFOMIS’s Basic Formal Ontology (BFO). With this project we aim to move beyond the level of (...) controlled vocabularies to yield an ontology with the ability to support reasoning applications. Our general procedure has been the implementation of a meta-ontological definition space in which the definitions of all the concepts and relations in LinKBase® are standardized in a framework of first-order logic. In this paper we describe how this standardization has already led to an improvement in the LinKBase® structure that allows for a greater degree of internal coherence than ever before possible. We then show the use of this philosophical standardization for the purpose of mapping external databases to one another, using LinKBase® as translation hub, with a greater degree of success than possible hitherto. We demonstrate how this offers a genuine advance over other application ontologies that have not submitted themselves to the demands of philosophical scrutiny. LinKBase® is one of the world’s largest applications-oriented medical domain ontologies, and BFO is one of the world’s first philosophically driven reference ontologies. The collaboration of the two thus initiates a new phase in the quest to solve the so-called “Tower of Babel”. (shrink)

Preference queries from databases aim to retrieve the best answers w.r.t. user's requirements. The integration of preferences in database queries has known many advances in the last decade. Most of works however are based on comparative preference statements obeying more or less strong semantics. Representing and reasoning about comparative preference statements has also been widely investigated in Artificial Intelligence. In this paper, we bridge the two frameworks and develop a simple and unified framework to reason about preferences in (...) class='Hi'>database queries. Our framework is based on insights from non-monotonic reasoning. (shrink)

This chapter argues on purely computational grounds that binary preferences cannot constitute the primitive evaluative data structure employed by evaluative cognition. The only way to make evaluative cognition work is to have a database of “computationally primitive values” from which other values not included in the database can be computed. This is called “the database calculation”. This is the only way to avoid having to store more values than it is possible to store. For such computations to (...) make sense, the computationally primitive values must be stored in such a way that it makes sense to perform mathematical computations on the values. The obvious way to do this is to store them in the form of a real-valued cardinal measure. However, for rational decision making, agents must have introspective access to the stored values, and humans cannot introspect real-valued measures of values. (shrink)

Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects. To study (...) the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery. We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics. The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources. The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well. Key Features: Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science Written by internationally leading researchers in the field of pure and applied logic Combines mathematical theory of modal logic and applications in artificial intelligence and computer science Numerous open problems for further research Well illustrated with pictures and tables. (shrink)

This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical (...) theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses the history of paraconsistent logic; language, negation, contradiction, consistency and inconsistency; logics of formal inconsistency and the main paraconsistent propositional systems; many-valued companions, possible-translations semantics and non-deterministic semantics; paraconsistent modal logics; first-order paraconsistent logics; applications to information processing, databases and quantum computation; and applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning. (shrink)

A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database (...) queries, with additional coverage of introductory material such as sets. Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. Reduced mathematical rigour to fit the needs of undergraduate students. (shrink)