The notion of program verification appears to trade upon an equivocation. Algorithms, as logical structures, are appropriate subjects for deductive verification. Programs, as causal models of those structures, are not. The success of program verification as a generally applicable and completely reliable method for guaranteeing program performance is not even a theoretical possibility.

In this paper I attempt to cast the current program verification debate within a more general perspective on the methodologies and goals of computer science. I show, first, how any method involved in demonstrating the correctness of a physically executing computer program, whether by testing or formal verification, involves reasoning that is defeasible in nature. Then, through a delineation of the senses in which programs can be run as tests, I show that the activities of testing (...) and formal verification do not necessarily share the same goals and thus do not always constitute alternatives. The testing of a program is not always intended to demonstrate a program's correctness. Testing may seek to accept or reject nonprograms including algorithms, specifications, and hypotheses regarding phenomena. The relationship between these kinds of testing and formal verification is couched in a more fundamental relationship between two views of computer science, one properly containing the other. (shrink)

A proof of ‘correctness’ for a mathematical algorithm cannot be relevant to executions of a program based on that algorithm because both the algorithm and the proof are based on assumptions that do not hold for computations carried out by real-world computers. Thus, proving the ‘correctness’ of an algorithm cannot establish the trustworthiness of programs based on that algorithm. Despite the (deceptive) sameness of the notations used to represent them, the transformation of an algorithm into an executable program (...) is a wrenching metamorphosis that changes a mathematical abstraction into a prescription for concrete actions to be taken by real computers. Therefore, it is verification of program executions (processes) that is needed, not of program texts that are merely the scripts for those processes. In this view, verification is the empirical investigation of: (a) the behavior that programs invoke in a computer system and (b) the larger context in which that behavior occurs. Here, deduction can play no more, and no less, a role than it does in the empirical sciences. (shrink)

Theorem 1 states a negative result about the classical semantics j= ! of program schemes. Theorem 2 investigates the reason for this. We conclude that Theorem 2 justies the Henkin-type semantics j= for which the opposite of the present Theorem 1 was proved in [1]{[3] and also in a dierent form in part III of [5]. The strongest positive result on j= is Corollary 6 in [3].

How are the properties of computer programs proved? We discuss three approaches in this article: inductive invariants, functional semantics, and explicit semantics. Because the first approach has received by far the most attention, it has produced the most impressive results to date. However, the field is now moving away from the inductive invariant approach.

The issue of proper functioning of operative computing and the utility of program verification, both in general and of specific methods, has been discussed a lot. In many of those discussions, attempts have been made to take mathematics as a model of knowledge and certitude achieving, and accordingly infer about the suitable ways to handle computing. I shortly review three approaches to the subject, and then take a stance by considering social factors which affect the epistemic status of (...) both mathematics and computing. I use the analogy between mathematics and computing in reverse—that is to say, I consider operative computing as a form of making mathematics, and so attempt to learn from computing to mathematics in general. I conclude that mathematics engineering is a field to be both developed for practical improvement of doing mathematics and taken into consideration while philosophizing about mathematics as well. (shrink)

Fetzer famously claims that program verification is not even a theoretical possibility, and offers a certain argument for this far-reaching claim. Unfortunately for Fetzer, and like-minded thinkers, this position-argument pair, while based on a seminal insight that program verification, despite its Platonic proof-theoretic airs, is plagued by the inevitable unreliability of messy, real-world causation, is demonstrably self-refuting. As I soon show, Fetzer is like the person who claims: ‘My sole claim is that every claim expressed by (...) an English sentence and starting with the phrase “My sole claim” is false’. Or, more accurately, such thinkers are like the person who claims that modus tollens is invalid, and supports this claim by giving an argument that itself employs this rule of inference. (shrink)

A debate over the theoretical capabilities of formal methods in computer science has raged for more than two years now. The function of this paper is to summarize the key elements of this debate and to respond to important criticisms others have advanced by placing these issues within a broader context of philosophical considerations about the nature of hardware and of software and about the kinds of knowledge that we have the capacity to acquire concerning their performance.

This paper provides a review of Raymond Turner’s book Computational Artefacts. Towards a Philosophy of Computer Science. Focus is made on the definition of program correctness as the twofold problem of evaluating whether both the symbolic program and the physical implementation satisfy a set of specifications. The review stresses how these are not two separate problems. First, it is highlighted how formal proofs of correctness need to rely on the analysis of physical computational processes. Secondly, it is underlined (...) how software testing requires considering the formal relations holding between the specifications and the symbolic program. Such a mutual dependency between formal and empirical program verification methods is finally shown to influence the debate on the epistemological status of computer science. (shrink)

Vardi, M.Y., Verification of concurrent programs: the automata-theoretic framework, Annals of Pure and Applied Logic 51 79–98. We present an automata-theoretic framework to the verification of concurrent and nondeterministic programs. The basic idea is that to verify that a program P is correct one writes a program A that receives the computation of P as input and diverges only on incorrect computations of P. Now P is correct if and only if a program PA, obtained (...) by combining P and A, terminates. We formalize this idea in a framework of ω-automata with a recursive set of states. This unifies previous works on verification of fair termination and verification of temporal properties. (shrink)

This study developed an online career adaptability improvement program as part of the undergraduate curriculum to improve college students’ career adaptability and verify its effectiveness. This 13-week intervention program, developed using the Korea-Career Adaptability Scale, consists of three domains: knowledge and recognition of the self and work environment, self-directed coping related to career behavior, and environmental interaction for career decisions and adaptation. Two sub-studies were conducted to achieve the research objectives: Study 1 included developing and testing a pilot (...) program and Study 2 quantitatively analyzed the final program to test its effectiveness. In Study 1, preliminary program development and validity were verified, and in Study 2, the effectiveness of the final program was verified. As a strategy to achieve the research purpose, in Study 1, literature review and needs analysis, program design reflecting the results of the needs analysis, validity verification through Delphi survey, preliminary program implementation and evaluation, and the operation of the final program were performed. To test the effectiveness of the program in Study 2, a pre-posttest of career adaptability was conducted on experimental, comparison, and control groups using the non-equivalent group pretest–posttest design, followed by a program satisfaction survey. This study is meaningful in that it developed an online program to help college students improve career adaptability and identified its effectiveness. This study yielded two results. First, it successfully developed a career adaptability improvement program for undergraduate students, wherein the career development tasks, and the sub-factors of career adaptability were organically interlinked. Second, it verified the statistically significant differences in the career adaptability scores among the experimental, comparison, and control groups. The highest mean score was obtained by participants in the experimental group, followed by the comparison and the control group. (shrink)

This paper traces a relatively linear sequence of early research approaches to the formal verification of concurrent programs. It does so forwards and then backwards in time. After briefly outlining the context, the key insights from three distinct approaches from the 1970s are identified (Ashcroft/Manna, Ashcroft (solo) and Owicki). The main technical material in the paper focuses on a specific program taken from the last published of the three pieces of research (Susan Owicki’s): her own verification of (...) her _Findpos_ example is outlined followed by attempts at verifying the same example using the earlier approaches. Reconsidering the prior approaches on the basis of Owicki’s useful example illuminates similarities and differences between the proposals. Along the way, observations about interactions between researchers (and some “blind spots”) are noted. (shrink)

Mathematical statements arising from program verification are believed to be much easier to deal with than statements coming from serious mathematics. At least this is true for “normal programming”.

This paper studies the complexity of behavior of multi-agent systems. Behavior properties are formulated using classical temporal logic languages and are checked with respect to the transition system induced by the definition of the multi-agent system. We establish various tight complexity bounds of the behavior properties under natural structural and semantic restrictions on agent programs and actions.

The main result of this paper belongs to the field of the comparative study of program verification methods as well as to the field called nonstandard logics of programs. We compare the program verifying powers of various well-known temporal logics of programs, one of which is the Intermittent Assertions Method, denoted as Bur. Bur is based on one of the simplest modal logics called S5 or sometime-logic. We will see that the minor change in this background modal (...) logic increases the program verifying power of Bur. The change can be described either technically as replacing the reflexive version of S5 with an irreflexive version, or intuitively as using the modality some-other-time instead of sometime. Some insights into the nature of computational induction and its variants are also obtained. (shrink)

Biró, B. and I. Sain, Peano arithmetic as axiomatization of the time frame in logics of programs and in dynamic logics, Annals of Pure and Applied Logic 63 201-225. We show that one can prove the partial correctness of more programs using Peano's axioms for the time frames of three-sorted time models than using only Presburger's axioms, that is it is useful to allow multiplication of time points at program verification and in dynamic and temporal logics. We organized (...) the paper as follows: 1. Preliminaries, 2. The main result, 3. Peano arithmetic with bounded multiplication, 4. Connections with temporal logics and dynamic logics, Acknowledgements, References. (shrink)

Almost all existing genetic programming systems deal with fitness evaluation solely by testing. In this paper, by contrast, we present an original approach that combines genetic programming with Hoare logic with the aid of model checking and finite state automata, henceby proposing a brand new verification-focused formal genetic programming system that makes it possible to evolve reliable programs with mathematicallyverified properties.

Introduction -- Algorithms, programs, procedures, and abstract automata -- Functioning of algorithms and automata, computation, and operations with algorithms and automata -- Basic postulates and axioms for algorithms -- Power of algorithms and classes of algorithms: comparison and evaluation -- Computing, accepting, and deciding modes of algorithms and programs -- Problems that people solve and related properties of algorithms -- Boundaries for algorithms and computation -- Software and hardware verification and testing -- Conclusion.

We present an initial and elementary investigation of the formal specification and mechanical verification of programs that interact with environments. We describe a formal, mechanically produced proof that a simple, real time control program keeps a vehicle on a straightline course in a variable crosswind. To formalize the specification we define a mathematical function which models the interaction of the program and its environment. We then state and prove two theorems about this function: the simulated vehicle never (...) gets farther than three units away from the intended course and homes to the course if the wind ever remains steady for at least four sampling intervals. (shrink)

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)

Doctoral programs at U.S. universities play a critical role in the development of human resources both in the United States and abroad. This volume reports the results of an extensive study of U.S. research-doctorate programs in five broad fields: physical sciences and mathematics, engineering, social and behavioral sciences, biological sciences, and the humanities. Research-Doctorate Programs in the United States documents changes that have taken place in the size, structure, and quality of doctoral education since the widely used 1982 editions. This (...) update provides selected information on nearly 4,000 doctoral programs in 41 subdisciplines at 274 doctorate-granting institutions. This volume also reports the results of the National Survey of Graduate Faculty, which polled a sample of faculty for their views on the scholarly quality of program faculty and the effectiveness of doctoral programs in preparing research scholars/scientists. This much-anticipated update of such an essential reference will be useful to education administrators, university faculty, and students seeking authoritative information on doctoral programs. (shrink)

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be found in human reasoning. (...) Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)

"An important contribution to contemporary jurisprudential debate and to legal thought more generally, Just Interpretations is far ahead of currently available work."--Peter Goodrich, author of Oedipus Lex "I was struck repeatedly by the clarity of expression throughout the book. Rosenfeld's description and criticism of the recent work of leading thinkers distinguishes his work within the legal theory genre. Furthermore, his own theory is quite original and provocative."--Aviam Soifer, author of Law and the Company We Keep.

This volume presents a collection of refereed papers reflecting the state of the art in the area of over-constrained systems. Besides 11 revised full papers, selected from the 24 submissions to the OCS workshop held in conjunction with the First International Conference on Principles and Practice of Constraint Programming, CP '95, held in Marseilles in September 1995, the book includes three comprehensive background papers of central importance for the workshop papers and the whole field. Also included is an introduction by (...) one of the volume editors together with a bibliography listing 243 entries. All in all this is a very useful reference book relevant for all researchers and practitioners interested in hierarchical, partial, and over-constrained systems. (shrink)

An understanding of logic is essential to computer science. This book provides a highly accessible account of the logical basis required for reasoning about computer programs and applying logic in fields like artificial intelligence. The text contains extended examples, algorithms, and programs written in Standard ML and Prolog. No prior knowledge of either language is required. The book contains a clear account of classical first-order logic, one of the basic tools for program verification, as well as an introductory (...) survey of modal and temporal logics and possible world semantics. An introduction to intuitionistic logic as a basis for an important style of program specification is also featured in the book. (shrink)

A new approach for defining causality and such related notions as degree of responsibility, degrees of blame, and causal explanation. Causality plays a central role in the way people structure the world; we constantly seek causal explanations for our observations. But what does it even mean that an event C "actually caused" event E? The problem of defining actual causation goes beyond mere philosophical speculation. For example, in many legal arguments, it is precisely what needs to be established in order (...) to determine responsibility. The philosophy literature has been struggling with the problem of defining causality since Hume. In this book, Joseph Halpern explores actual causality, and such related notions as degree of responsibility, degree of blame, and causal explanation. The goal is to arrive at a definition of causality that matches our natural language usage and is helpful, for example, to a jury deciding a legal case, a programmer looking for the line of code that cause some software to fail, or an economist trying to determine whether austerity caused a subsequent depression. Halpern applies and expands an approach to causality that he and Judea Pearl developed, based on structural equations. He carefully formulates a definition of causality, and building on this, defines degree of responsibility, degree of blame, and causal explanation. He concludes by discussing how these ideas can be applied to such practical problems as accountability and program verification. Technical details are generally confined to the final section of each chapter and can be skipped by non-mathematical readers. (shrink)

Prominent experts present papers which discuss problems regarding this subject. Coverage includes case studies in the translation of logics for second-order and propositional dynamic logic; many-sorted algebras and equational logic; logical foundations of artificial intelligence along with a variety of methods that exist to encode information; program verification techniques such as Floyd-Hoare, intermittent assertion and temporal logic of programs.

This paper is concerned with techniques for identifying simple and quantified lattice points in 2SAT polytopes. 2SAT polytopes generalize the polyhedra corresponding to Boolean 2SAT formulas, Vertex-Packing and Network flow problems; they find wide application in the domains of Program verification and State-Space search . Our techniques are based on the symbolic elimination strategy called the Fourier-Motzkin elimination procedure and thus have the advantages of being extremely simple and incremental. We also provide a characterization of a 2SAT polytope (...) in terms of its extreme points and derive some interesting hardness results for associated optimization problems. Finally, we provide a brief discussion on the maximum size of a subdeterminant of the linear system representing a 2SAT polytope; this parameter plays a vital role in deriving analytical bounds on the size of the search space for checking whether the polyhedron includes a lattice point. (shrink)

In this dissertation, we construct a consistent, complete quotational logic G$\sb1$. We first develop a semantics, and then show the undecidability of circular quotation and anaphorism . Next, a complete axiom system is presented, and completeness theorems are shown for G$\sb1$. We show that definable truth exists in G$\sb1$. ;Later, we replace equality in G$\sb1$ with an equivalence relation. An axiom system and completeness theorems are provided for this equality-free version of G$\sb1$, which is useful in program verification. (...) ;Interpolation and definability are discussed in intensional and extensional contexts. We show that G$\sb1$ contains the complete first order theory of arithmetic by implicit definitional extension. ;The last chapter deals with representability and fixed points. Derived induction schemata are produced, and G$\sb1$ is shown to be a recursion theory. We give an example of how G$\sb1$ may be used to solve domain equations of Scott. (shrink)

We devise imperative programming languages for verified real number computation where real numbers are provided as abstract data types such that the users of the languages can express real number computation by considering real numbers as abstract mathematical entities. Unlike other common approaches toward real number computation, based on an algebraic model that lacks implementability or transcendental computation, or finite-precision approximation such as using double precision computation that lacks a formal foundation, our languages are devised based on computable analysis, a (...) foundation of rigorous computation over continuous data. Consequently, the users of the language can easily program real number computation and reason about the behaviours of their programs, relying on their mathematical knowledge of real numbers without worrying about artificial roundoff errors. As the languages are imperative, we adopt precondition–postcondition-style program specification and Hoare-style program verification methodologies. Consequently, the users of the language can easily program a computation over real numbers, specify the expected behaviour of the program, including termination, and prove the correctness of the specification. Furthermore, we suggest extending the languages with other interesting continuous data, such as matrices, continuous real functions, et cetera.Abstract taken directly from the thesis.E-mail: [email protected]: https://sewonpark.com/thesis. (shrink)

In this paper we study automated reasoning in the modal logic CPDLreg which is a combination of CPDL (Propositional Dynamic Logic with Converse) and REGc (Regular Grammar Logic with Converse). The logic CPDL is widely used in many areas, including program verification, theory of action and change, and knowledge representation. On the other hand, the logic REGc is applicable in reasoning about epistemic states and ontologies (via Description Logics). The modal logic CPDLreg can serve as a technical foundation (...) for reasoning about agency. Even very rich multi-agent logics can be embedded into CPDLreg via a suitable translation. Therefore, CPDLreg can serve as a test bed to implement and possibly verify new ideas without providing specific automated reasoning techniques for the logic in question. This process can to a large extent be automated. The idea of embedding various logics into CPDLreg is illustrated on a rather advanced logic TEAMLOGK designed to specify teamwork in multi-agent systems. Apart from defining informational and motivational attitudes of groups of agents, TEAMLOGK allows for grading agents' beliefs, goals and intentions. The current paper is a companion to our paper (Dunin-Kęplicz et al., 2010a). The main contribution are proofs of soundness and completeness of the tableau calculus for CPDLreg provided in (Dunin-Kęplicz et al., 2010a). (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have (...) been expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

The prelims comprise: Introduction Computer Science and Mathematics The Formal Verification Debate Abstraction in Computer Science Conclusion.

The verification of a sentence against a visual display in experimental conditions reveals a procedure that is driven solely by the properties of the linguistic input and not by the properties of the context (the set-up of the visual display) or extra-linguistic cognition (operations executed to obtain the truth value). This procedure, according to the Interface Transparency Thesis (ITT) (Lidz et al. in Nat Lang Semant 19(3):227–256, 2011), represents the meaning of an expression at the interface with the ‘conceptual-intentional’ (...) system (Chomsky in The minimalist program. MIT Press, Cambridge, 1995). My experiments provide support for the ITT by replicating in Polish and in Bulgarian the findings of Lidz et al. (Nat Lang Semant 19(3):227–256, 2011) for the English quantifier most. We also obtain new evidence that participants are prompted to switch between verification procedures by a change in the linguistic input (a different superlative quantifier entailed by most), but not by a change in the visual input. Thus, the motivation for the subconscious switch in procedures is not to maximize efficiency. Participants use the procedure associated with each quantifier, and in effect, the same display is verified differently depending on which information the visual system is instructed to use by the semantic representation of the sentence. (shrink)

From the Philosophies journal program, one of the main aims of the journal is to help establish a new unity in diversity in human knowledge, which would include both “Wissen” (i.e., “Wissenschaft”) and “sc¯ıre” (i.e., “science”). As is known, “Wissenshaft” (the pursuit of knowledge, learning, and scholarship) is a broader concept of knowledge than “science”, as it involves all kinds of knowledge,including philosophy, and not exclusively knowledge in the form of directly testable explanations and predictions. The broader notion of (...) scholarship incorporates an understanding and articulation of the role of the learner and the process of the growth of knowledge and its development, rather than only the final product and its verification and validation. In other words, it is a form of knowledge that is inclusive of both short-term and long-term perspectives; it is local and global, critical and hypothetical (speculative), breaking new ground. This new synthesis or rather re-connection of knowledge is expected to resonate with basic human value systems, including cultural values. Since knowledge tends to spontaneously fragment while it grows, we take existing diversity as a resource and a starting point for a new synthesis. The idea of broad, inclusive knowledge is in fact not so new. From the beginning, natural philosophy included all contemporary knowledge about nature. Newton was a natural philosopher, as were Bohr, Einstein, Prigogine, Weizsäcker, and Wheeler—to name but a few. Today, the unifying picture of the natural/physical world is sorely missing among the isolated silos of particular scientific domains, each with its own specific ontologies, methodologies, and epistemologies. From the profound need for connected and common knowledge, new trends towards synthesis have emerged in the last decades. One major theme is complexity, especially when applied to biology or medicine, which helps us to grasp the importance of connectedness between present-day disparate pieces of knowledge—frameworks, theories, approaches, etc. Related to this is the emergence of network science, which studies structures of nodes (actors) and edges as connections between them. This book is connecting work on contemporary natural philosophy and its connections with existing philosophies, sciences and other knowledge fields. (shrink)

Motivated by the verification of programs with pointer variables, we introduce a temporal logic whose underlying assertion language is the quantifier-free fragment of separation logic and the temporal logic on the top of it is the standard linear-time temporal logic LTL. We analyze the complexity of various model-checking and satisfiability problems for , considering various fragments of separation logic , various classes of models , and the influence of fixing the initial memory state. We provide a complete picture based (...) on these criteria. Our main decidability result is pspace-completeness of the satisfiability problems on the record fragment and on a classical fragment allowing pointer arithmetic. -completeness or -completeness results are established for various problems by reducing standard problems for Minsky machines, and underline the tightness of our decidability results. (shrink)