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Nomenclatura Unesco > (11) Lógica > (1103) Lógica general
Nomenclatura Unesco > (11) Lógica > (1103) Lógica general
Felty, Amy; Miller, Dale
Various forms of typed λ-calculi have been proposed as specification languages for representing wide varieties of object logics. The logical framework, LF, is an example of such a dependent-type λ-calculus. A small subset of intuitionistic logic with quantification over simply typed λ-calculus has also been proposed as a framework for specifying general logics. The logic of hereditary Harrop formulas with quantification at all non-predicate types, denoted here as hhω, is such a meta-logic that has been implemented in both the Isabelle theorem prover and the λProlog logic programming language. Both frameworks provide for specifications of logics in which details involved...
Cainghino, Chris; Sjoberg, Vilhelm; Weirich, Stephanie
The TRELLYS project has produced several designs for practical dependently typed languages. These languages are broken into two fragments—a logical fragment where every term normalizes and which is consistent when interpreted as a logic, and a programmatic fragment with general recursion and other convenient but unsound features. In this paper, we present a small example language in this style. Our design allows the programmer to explicitly mention and pass information between the two fragments. We show that this feature substantially complicates the metatheory and present a new technique, combining the traditional Girard–Tait method with step-indexed logical relations, which we use...
Caballero Roldán, Rafael
Declarative debugging is a debugging technique that abstracts the execution details to focus on the semantic meaning of the program components. It was frst proposed in the feld of Logic Programming, but its general structure has been later extended to other programming paradigms, becoming an active area of research. The technique relies on a data structure, the computation tree, that represents some computation producing an unexpected result. This tree is traversed by asking questions to the user about the correction of the intermediate computation steps until the source of the bug has been found. We show how instances of this...
Andreas Speck; Sven Feja; Marcel Schulz
Abstract. The behavior of commercial systems is described with busi-ness process models. There are different notations and formalism to ex-press business processes. Many of these notations such as BPMN or ARIS EPC models are widely used in commercial projects. In the paper we focus on formalisms to express rules and specifications for the business processes. Temporal logic in general is a suitable formal-ism to express rules for dynamic processes. CTL is one kind of temporal logic focusing on branches and paths in particular. With CTL it is possi-ble to formulate rules about different paths in business processes. Since the textual...
Interviews Shimshon Bichler; Jonathan Nitzan; Shimshon Bichler; Jonathan Nitzan; Timothy Dimuzio; Jonathan Nitzan
Tim Di Muzio: You argue that the capital as power framework does not offer a general theory of society but an incisive account of how capitalists shape and reshape our world through the logic of differential capitalization and accumulation. As you well know, the Occupy Wall Street movement has organized under the banner ‘We are the 99%’, opposing what they refer to as the global 1%. Could the capital as power framework be conceptualized as the political economy of the 1%? If not, do you see any way in which the capital as power framework could contribute to a critical...
Umberto Straccia
We present Annotated Answer Set Programming, that extends the expressive power of disjunctive logic programming with annotation terms, taken from the general-ized annotated logic programming framework.
DeHon, André; Wilson, Michael J.
How can Programmable Logic Arrays (PLAs) be built without relying on lithography to pattern their smallest features? In this paper, we detail designs which exploit emerging, bottom-up material synthesis techniques to build PLAs
using molecular-scale nanowires. Our new designs accommodate technologies where the only post-fabrication programmable element is a non-restoring diode. We introduce
stochastic techniques which allow us to restore the diode
logic at the nanoscale so that it can be cascaded and interconnected for general logic evaluation. Under conservative assumptions using 10nm nanowires and 90nm lithographic support, we project yielded logic density around 500,000nm^2/or term for a 60 or-term array; a complete...
Reinhard Muskens
In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalise to partial and paraconsistent logics once the right set-up is chosen. Our logic L4 has a semantics that also underlies Belnap’s [4] and is related to the...
Lars-henrik Eriksson
Abstract. We describe how the calculus of partial inductive definitions is used to represent logics. This calculus includes the powerful principle of definitional reflection. We describe two conceptually different approaches to representing a logic, both making essential use of definitional reflection. In the deductive approach, the logic is defined by its inference rules. Only the succedent rules (in a sequent calculus setting – introduction rules in a natural deduction setting) need be given. The other rules are obtained implicitly using definitional reflection. In the semantic approach, the logic is defined using its valuation function. The latter approach often provides a...
Peter Csaba; Ölveczky José Meseguer; Peter Csaba Ölveczky; José Meseguer
Abstract At present, designers of real-time systems face a dilemma between expressiveness and automatic verification: if they can specify some aspects of their system in some automaton-based formalism, then automatic verification is possible; but more complex system components may be hard or impossible to express in such decidable formalisms. These more complex components may still be simulated; but there is then little support for their formal analysis. The main goal of Real-Time Maude is to provide a way out of this dilemma, while complementing both decision procedures and simulation tools. Real-Time Maude emphasizes ease and generality of specification, including support...
Amy Felty; Dale Miller
Language Various forms of typed λ-calculi have been proposed as specification languages for representing wide varieties of object logics. The logical framework, LF, is an example of such a dependent-type λ-calculus. A small subset of intuitionistic logic with quantification over simply typed λ-calculus has also been proposed as a framework for specifying general logics. The logic of hereditary Harrop formulas with quantification at all non-predicate types, denoted here as hhω, is such a meta-logic that has been implemented in both the Isabelle theorem prover and the λProlog logic programming language. Both frameworks provide for specifications of logics in which details...
Sami Hautakangas; Tomi Kiilakoski
ABSTRACT The purpose of this article is to analyse the meaning of different cultural paradigms in the development of educational technology. The article analyses technology critically from the perspective of the philosophy of technology, examines the manifestations of instrumentalism in the curriculum theory and analyses its effects on the different levels of decision-making relative to the design processes of educational technology. It is claimed that instrumental rationality may increase if common curricular models are used when engineering technology. One major problem that affects the development is that instrumentalism and its manifestations on different levels of design and application of educational...
Abstract — We present a hardware verification environment that integrates the ACL2 theorem prover and SixthSense, the IBM internal formal verification tool. In this environment, SixthSense is called through an ACL2 function acl2six that makes use of a general-purpose external interface added to the ACL2 theorem prover. This interface allows connecting any decision procedures and model-checker to ACL2 by simply writing ACL2 functions. Our environment exploits a unique approach to connect the logic of general-purpose theorem prover and machine designs in VHDL, rather than a language embedding. With an example of a pipelined multiplier, we show how our environment can...
Louis Hodes
Using formal logic, many problems from the general area of linear inequalities can be expressed in the elementary theory of addition on the real numbers (EAR). We describe a method for eliminating quantifiers in EAR which has been programmed and demonstrate its usefulness in solving some problems related to linear programming. In the area of mechanical mathematics this kind of approach has been neglected in favor of more generalized methods based on Herbrand expansion. However, in a restricted area, such as linear inequalities, the use of these specialized methods can increase efficiency by several orders of magnitude over an axiomatic...
Montréal Québec; C. M. Sperberg-mcqueen
The W3C XML Schema specification is dense and sometimes hard to follow; some have suggested it would be better to write specifications in formal, executable languages, so that questions could be answered just by running the spec. But programs are themselves often even harder to understand. Representing schemas as logic grammars offers a better approach: logic grammars can mirror the wording of the XML Schema specification and, at the same time, provide a runnable implementation of it. Logic grammars are formal grammars written in logic-programming systems; in the implementation described here, logic grammars capture both the general rules of XML...
N. N. Morsi; W. B. Lotfallah; M. S. El-zekey
Recently, Morsi [28] has developed a complete syntax for the semantical domain of all adjointness algebras. In [1], Abdel-Hamid and Morsi enrich adjointness algebras with one more conjunction, this time a t-norm T (T need not be commutative) that ties an implication A in the following sense: A(T(a, b), z) = A(a, A(b, z)). In this paper, we develop a new complete syntax for quite a general multiple-valued logic whose semantics is based on this type of algebra. Such a formal system serves as a combined calculus for two, possibly different, types of uncertainty. 1 Tied Adjointness Algebras We here...
Daniel Sheridan
Abstract. Despite the widespread use and study of Boolean satisfiability for a diverse range of problem domains, encoding of problems is usually given to general propositional logic with little or no discussion of the conversion to clause form that will be necessary. In this paper we present a fast and easy to implement conversion to equisatisfiable clause form for Boolean circuits. Since the conversion is equivalent to that of Boy de la Tour it is optimal in the number of clauses produced. We present experimental results comparing this and other conversion procedures on BMC problems and conclude that the CNF...
Yulia S. Korukhova; Postgraduate Student
In [Manna and Waldinger, 1992] the deductive tableau method was proposed. It is appropriate for the synthesis of functional programs. The specification of a program is taken as a mathematical existence theorem and we prove the existence of an object that satisfies the specified conditions. Specification is based on predicate-logic, because it is quite general and appropriate for deductive methods. If other
Yan Zhang, Norman Y. Foo , et al.
We consider how to forget a set of atoms in a logic program. Intuitively, when a set of atoms is forgotten from a logic program, all atoms in the set should be eliminated from this program in some way, and other atoms related to them in the program might also be affected. We define notions of strong and weak forgettings in logic programs to capture such intuition and reveal their close connections to the notion of forgetting in classical propositional theories. Based on these notions, we then propose a framework for conflict solving in logic programs, which is general enough...
Marijn Heule; Hans Van Maaren
Abstract. This paper shows that idempotents in finite rings of integers can act as Generalized Boolean Assignments (GBA’s) by providing a completeness theorem. We introduce the notion of a generic Generalized Boolean Assignment. The mere propagation of such an assignment reveals feasibility (existence of a solution) of a formula in propositional logic. Then, we demystify this general concept by formulating the process on the bit-level: It turns out that propagation of a GBA only simulates bitwise (non-communicating) parallel computing. We capitalize on this by modifying the state-of-the-art local search Sat solver UnitWalk accordingly. This modification involves a more complicated parallelism....