applications of predicate logic in computer science

The existence of high performance algorithms for reasoning with propositional logic is the main reason for its wide use in computer science… Retrospectively, it appears that modern knowledge systems are the culmination of a steady linear development in the field of logic. Finally, the XPS may need to reason about which tasks to apply, and when. This book conveys instead, in an engaging tone, how logic gets put to work in computer science, covering usages of logic that range from the foundations for the infrastructure of computing to the design, testing and verification of programs. We use cookies to help provide and enhance our service and tailor content and ads. Although the need to be able to switch to a configuration with nonstandard components is a common problem in engineer-to-order settings, this approach was taken up very late in SAP configurators and has not been completely implemented to date. Local propagation can also be applied in the case of linear numeric inequalities/equalities with real-valued variables with interval domains (Haag, 1989). In a configuration involving birds, the soft constraint will apply in some situations, but may not apply in others. is not a default according to the definition above. If there were three instances of staircases in the configuration of a building with 50 posts each, it would need to be applied to 150 staircase/post pairs. In general, rules that come into conflict are as follows: For the event ev(A, B), the initial states A and B are the same and the next states are defined as follows. The propositional logic is not powerful enough to represent all types of assertions that are used in computer science and mathematics, or to express … Given a domain description, various types of commonsense reasoning can be performed. This means that a multitude of solutions exists and it is not hard to find one. In predicate logic a logical expression is defined as follows: (1) If t 1, t 2,…, t n are terms and P is a predicate with n parameters, then P (t 1, t 2, …, t n) is an atomic formula and a logical expression. It was later adopted by SAP and is still in use today. Let us call such rules of inference open defaults. This structure will open up the knowledge and workings of humankind to meaningful analysis by software agents, providing a new class of tools by which we can live, work and learn together (Berners-Lee, Hendler and Lassila 2001). In mathematical logic, a predicate is commonly understood to be a Boolean-valued function P: X → {true, false}, called a predicate on X. A configuration is valid if it is consistent and a set of completeness axioms related to CONF is fulfilled. Once a value has been assigned to the variable , the statement becomes a proposition and has a truth or false(tf) value. Not all constraints are created equal. In this case a call forwarding variable is chosen. The declarative representation as such is called a (configuration) model (see Hotz et al., 2014a3). A configuration CONF is described by a set of positive ground literals whose predicate symbols are in CLANG.Definition Configuration (Solution)Given a configuration task (CKB,REQ,CLANG), a configuration CONF is consistent if and only if CKB∪REQ∪CONF is satisfiable. Our plan will be to translate the word problem for a Thue process into predicate logic in such a way that a solution to Hilbert's satisfiability problem would also yield a solution to the word problem for the given process. The predicate can be considered as a function. Section 3 explores the first of a number of ways of encoding a source logic into a target logic: syntactic encodings; we discuss the basic ideas and consider the merits of the approach from an automated reasoning point of view. The event calculus uses the default assumptions that (1) the only events that occur are those known to occur and (2) the only effects of events are those that are known. A default schema looks like a default, the only difference being that φ, Ψ1, ………, Ψn, χ are arbitrary predicate logic formulae (i.e. Sometimes a dependency cannot be expressed as a constraint in the model with a given finite set of variables. Its unifying logical language will enable these concepts to be progressively linked into a universal Web. Temporal logics are being used in computer engineering, in software verification. It begins with the discussion of propositional logic, giving two constraint-based algorithms for solving the satisfiability problem, called "linear" and "cubic" (I don't get it - how can an NP-complete problem have a cubic algorithm, unless P=NP? In this case, the preferences or optimality criteria need to be defined somehow. In a model-based XPS, this representation should be declarative wherever possible. There is a vocabulary W such that there is no algorithm for testing a given W-sentence to determine whether it is satisfiable. Resolving inconsistency is a problem of discarding soft justifications, not soft constraints overall. Therefore conflict resolution is needed. Liam Magee, in Towards a Semantic Web, 2011. Albert Haag, in Knowledge-Based Configuration, 2014. When the constraint is applied, its variables are bound to the corresponding properties (values or domains) of object instances in the configuration. In TEX-K this was not directly part of the constraint processing, but rather a topic considered under the heading of controlling the configuration process (Günter et al., 1990; see Hotz and Günter, 201413). MIT Press began publishing journals in 1970 with the first volumes of Linguistic Inquiry and the Journal of Interdisciplinary History. Today we publish over 30 titles in the arts and humanities, social sciences, and science and technology. Introduction to Predicate Logic. We will focus mainly on matters related to expressive power and reasoning tasks; specific questions that we will be concerned with are: What are the different options for encoding the formulae in predicate logic? This means it is not possible to find a solution that satisfies all these constraints. To avoid this problem, many of the subsequent approaches to configuration in the 1980s have a basis in predicate logic. Can we exploit special features of the source logic to enhance the encoding? (Lenzen 2004, p. 1). These are typically fulfilled in good solutions, but might be dropped if violated, and are termed soft constraints. Call waiting service (Figure 9.13): When terminal A calls terminal B while terminal B and terminal C are talking to each other, the system lets terminal B know of the arrival of the call. The search for an actual solution, perhaps requiring the formulation of suitable heuristics, was considered as a separate problem and not a topic of constraints themselves. It has many practical applications in computer science like design of computing machines, artificial intelligence, definition of data structures for programming languages etc. Since (at least in interactive configuration) the XPS must make the distinction between inconsistency and incompleteness clear to the user, it is opportune to distinguish such dependencies from constraints; they were referred to as checks in Haag (1991). A term can contain individual constants, individual variables, and/or functions. In the preceding example, each cabinet consumes space equal to its width and the overall kitchen provides the amount of available space W. SAP followed the approach of Bernhard Neumann who developed a concept of balances for resources and/or functionality in hierarchical configurations in his dissertation (Neumann, 1989). Some constraints encode physical or legal laws that must not be violated. Table 6.6. This implies that. The rules that do not come into conflict are: The initial states of the foregoing descriptions are not the same, which means there is no conflict. CONF together with the corresponding completeness axioms is denoted as CONF^=CONF∪AX. The complexity of this is high in practice and exponential in theory. Conflict resolution (see Figure 9.15 for examples of service descriptions that come into conflict and the rules by which such conflicts are resolved): When an event dial(A, B) occurs, system checks states A and B. A defaultδ has the form. In general, a statement involving n variables can be denoted by . “Many other books present logic as an object of study. The first steps in weaving the semantic web into the structure of the existing Web are already under way. From the beginning of the field it was realized that technology to automate logical inferences could have great potential to solve problems and draw conclusions from facts. To illustrate these concepts: assume the angle of ascension is 45∘ (tanα=1) and the height of the handrail is 75cm, and the steps are 32cm deep, then the variable pos (position of the post on the step) is restricted (without considering further constraints) to the interval [0,32]cm and, consequently, the constraint can restrict the variable hp (the height of the post) to [75,107]cm. Finding this autonomously may be the task of the XPS. A configuration task can be defined as a triple (CKB,REQ,CLANG) where CKB and REQ are sets of logical sentences and CLANG is a set of predicate symbols. Finally, in Section 8 we formulate some conclusions and open questions. Let Π have the productions gi → hi, i = 1,2,…, K, together with their inverses, where we may assume that for each i, gi, hi ≠ 0 (recall Theorem 3.5 in Chapter 7). In general, a conflict occurs when the initial states and operations of two or more rules are the same. Here the functional symbol g shows the relationship between z and w. A predicate symbol represents a predicate for objects and is notated P(x, y), Q(z),…, where P and Q are predicate symbols. A justification is an implication f1…fn→f that states that the fact f is a valid part of the configuration if the facts f1…fn are valid. The power of intuitionistic logic lies in the effectiveness or constructiveness of its conclusions. Indeed, as the quote from Hegel suggests, at the start of the nineteenth century, logic was perceived to be a field for the most part exhausted by Aristotle’s exposition of syllogisms. No sense to solve for α. all these constraints and would destroy the result of the approaches. 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