We argue from the Church-Turing thesis (Kleene Mathematical logic. New York: Wiley 1967) that a program can be considered as equivalent to a formal language similar to predicate calculus where predicates can be taken as functions. We can relate such a calculus to Wittgenstein’s first major work, the Tractatus, and use the Tractatus and its theses as a model of the formal classical definition of a computer program. However, Wittgenstein found flaws in his initial great work and he explored these (...) flaws in a new thesis described in his second great work; the Philosophical Investigations. The question we address is “can computer science make the same leap?” We are proposing, because of the flaws identified by Wittgenstein, that computers will never have the possibility of natural communication with people unless they become active participants of human society. The essential difference between formal models used in computing and human communication is that formal models are based upon rational sets whereas people are not so restricted. We introduce irrational sets as a concept that requires the use of an abductive inference system. However, formal models are still considered central to our means of using hypotheses through deduction to make predictions about the world. These formal models are required to continually be updated in response to peoples’ changes in their way of seeing the world. We propose that one mechanism used to keep track of these changes is the Peircian abductive loop. (shrink)

The effective reasoning capability of an agent can be defined as its capability to infer, within a given space and time bound, facts that are logical consequences of its knowledge base. In this paper we show how to determine the effective reasoning capability of an agent with limited memory by encoding the agent as a transition system and automatically verifying whether a state where the agent believes a certain conclusion is reachable from the start state. We present experimental results using (...) the Model Based Planner (MBP) which illustrates how the length of the deduction varies for different memory sizes. (shrink)

The application of digital humanities techniques to philosophy is changing the way scholars approach the discipline. This paper seeks to open a discussion about the difficulties, methods, opportunities, and dangers of creating and utilizing a formal representation of the discipline of philosophy. We review our current project, the Indiana Philosophy Ontology (InPhO) project, which uses a combination of automated methods and expert feedback to create a dynamic computational ontology for the discipline of philosophy. We argue that our distributed, expert-based approach (...) to modeling the discipline carries substantial practical and philosophical benefits over alternatives. We also discuss challenges facing our project (and any other similar project) as well as the future directions for digital philosophy afforded by formal modeling. (shrink)

A sequence generator is a finite graph, more general than, but akin to, the usual state diagram associated with a finite automaton. The nodes of a sequence generator represent complete states, and each node is labeled with an input and an output state. An element of the behavior of a sequence generator is obtained by taking the input and output states along an infinite path of the graph.Sequence generators may be associated with formulas of the monadic predicate calculus, in which (...) the individual variables range over the times 0, 1, 2, 3, [middle dot][middle dot][middle dot], and the predicate variables represent complete states, input states, and output states. An unrestricted singulary recursion is a formula in which the complete state at time [tau] + 1 is expressed as a truth-function of the complete state at time [tau] and the input states from times [tau] + 1 to [tau] + h. Necessary and sufficient conditions are given for a formula derived from a sequence generator being equivalent to an unrestricted singulary recursion. (shrink)

1. Logic programming did not seize the attention of most programmers until the Japanese announced that they had chosen Prolog for their ambitious Fifth Generation Computer Systems project. While that project appeàrs now to be hampered by bureaucratic difficulties, the interest it aroused in Prolog lives on. Part of the attraction of Prolog stems from the fact that the beginner will very quickly be able to write toy programs, even spectacular ones. Difficulties in creating larger programs, however, seem to bring (...) back Prolog to the level of other programming languages. Such difficulties arise from numerous defects of Prolog, some of which are purely logicai in nature. Among the latter at least two should be mentioned: (a) the peculiar meaning of negation; (b) the fact that reduction to clausal form is not part of the language. As to (a), strictly speaking Prolog has no negation. Its notion ot.negation- as-failure - by which -i <p is inferred from fatture to infer y - is a tricky one. For instance, suppose that the goal likes (John, X ) succeeds with X instantiated to mary. Then not (likes (John, X )) fails, so X becomes uninstantiated and hence has no value. However not (not (likes (John, X ))) succeeds with X instantiated to mary. This makes the meaning of negation almost incomprehensible. As to (b), for efficiency Prolog uses the programmer, as it were, as a preprocessor for reduction to clausal form: with the gain in efficiency that one can very well imagine. Of course reduction to clausal form can be implemented in Prolog and bùilt up within every Prolog program together with a suitable user interface, but this is very much like designing a new programming language. (shrink)

Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions ...

Partial functions are ubiquitous in both mathematics and computer science. Therefore, it is imperative that the underlying logical formalism for a general-purpose mechanized mathematics system provide strong support for reasoning about partial functions. Unfortunately, the common logical formalisms — first-order logic, type theory, and set theory — are usually only adequate for reasoning about partial functionsin theory. However, the approach to partial functions traditionally employed by mathematicians is quite adequatein practice. This paper shows how the traditional approach to partial functions (...) can be formalized in a range of formalisms that includes first-order logic, simple type theory, and Von-Neumann—Bernays—Gödel set theory. It argues that these new formalisms allow one to directly reason about partial functions; are based on natural, well-understood, familiar principles; and can be effectively implemented in mechanized mathematics systems. (shrink)

Medical expert systems (MES) are knowledge-based computer programs that are designed for advising physicians on diagnostical and therapeutical decision-making. They use heuristic methods developed by Artificial Intelligence researchers in order to retrieve from large knowledge-bases information needed in the situation. Constructing the knowledge-base of a MES embraces the problem of explicating and fixing the conceptual, causal and epistemic relations between a lot of medical objects. There is a number of preconditions which any adequate representation of such knowledge must fulfil, among (...) them the conditions of consistency, of completeness, of unequivocality, etc. Existing systems for classification and coding, like ICD and SNOMED, are not designed for the needs of constructing expert systems or, more generally, of knowledge processing and knowledge engineering. Their syntax is not sufficiently rich for expressing the more complex structures of (medical) knowledge. What is needed, is a language that can be used for expressing logical and descriptive relations between medical objects and facts, approximately at the level of the language of second order predicate logic. Simultaneously, it must be possible to process this language at the machine level. This can be achieved by using some dialects of the programming language LISP or, particularly, by using the programming language PROLOG. Thus, in order to achieve a suitable classification system, it is necessary to develop a system of medical data structures and predicates expressed in LISP or PROLOG. (shrink)

Abstract State Machines (ASMs) provide a formal method for transparent design and specification of complex dynamic systems. They combine advantages of informal and formal methods. Applications of this method motivate a number of computability and decidability problems connected to ASMs. Such problems result for example from the area of verifying properties of ASMs. Their high expressive power leads rather directly to undecidability respectively uncomputability results for most interesting problems in the case of unrestricted ASMs. Consequently, it is rather natural to (...) ask whether there exist expressive classes of ASMs for which we can prove positive decidability and computability results. In this work, we introduce such a class of ASMs. The concept is similar to the one of the guarded fragment of first-order logic. We analyze the expressive power of this class and prove that it is stronger than Datalog LITE and the guarded fragment of first-order fixed point logic. Some decidability and computability results have been proven in earlier works. (shrink)

Images in Computer Science: Clarifications Required. The Age of the Images Images take a rather prominent place in contemporary life in the western ...