A generalized small model property for languages which force the infinity

This paper deals with formulas of set theory which force the infinity. For such formulas, we provide a technique to infer satisfiability from a finite assignment.Comment: 21 pages. to appear on "Le Matematiche

A Decidable Timeout based Extension of Propositional Linear Temporal Logic

We develop a timeout based extension of propositional linear temporal logic (which we call TLTL) to specify timing properties of timeout based models of real time systems. TLTL formulas explicitly refer to a running global clock together with static timing variables as well as a dynamic variable abstracting the timeout behavior. We extend LTL with the capability to express timeout constraints. From the expressiveness view point, TLTL is not comparable with important known clock based real-time logics including TPTL, XCTL, and MTL, i.e., TLTL can specify certain properties, which cannot be specified in these logics (also vice-versa). We define a corresponding timeout tableau for satisfiability checking of the TLTL formulas. Also a model checking algorithm over timeout Kripke structure is presented. Further we prove that the validity checking for such an extended logic remains PSPACE-complete even in the presence of timeout constraints and infinite state models. Under discrete time semantics, with bounded timeout increments, the model-checking problem that if a TLTL-formula holds in a timeout Kripke structure is also PSPACE complete. We further prove that when TLTL is interpreted over discrete time, it can be embedded in the monadic second order logic with time, and when TLTL is interpreted over dense time without the condition of non-zenoness, the resulting logic becomes $\Sigma_1^1$-complete

IDEF3 formalization report

The Process Description Capture Method (IDEF3) is one of several Integrated Computer-Aided Manufacturing (ICAM) DEFinition methods developed by the Air Force to support systems engineering activities, and in particular, to support information systems development. These methods have evolved as a distillation of 'good practice' experience by information system developers and are designed to raise the performance level of the novice practitioner to one comparable with that of an expert. IDEF3 is meant to serve as a knowledge acquisition and requirements definition tool that structures the user's understanding of how a given process, event, or system works around process descriptions. A special purpose graphical language accompanying the method serves to highlight temporal precedence and causality relationships relative to the process or event being described

The Automation of Syllogistic II. Optimization and Complexity Issues

In the first paper of this series it was shown that any unquantified formula p in the collection MLSSF (multilevel syllogistic extended with the singleton operator and the predicate Finite) can be decomposed as a disjunction of set-theoretic formulae called syllogistic schemes. The syllogistic schemes are satisfiable and no two of them have a model in common, therefore the previous result already implied the decidability of the class MLSSF by simply checking if the set of syllogistic schemes associated with the given formula is empty. In the first section of this paper a new and improved searching algorithm for syllogistic schemes is introduced, based on a proof of existence of a 'minimum effort' scheme for any given satisfiable formula in MLSF. The algorithm addressed above can be piloted quite effectively even though it involves backtracking. In the second part of the paper, complexity issues are studied by showing that the class of ( 00)o1-simple prenex formulae (an extension of MLS) has a decision problem which is NP-complete. The decision algorithm that proves the membership of this decision problem to NP can be seen as a different decision algorithm for ML

Partial Quantifier Elimination By Certificate Clauses

We study partial quantifier elimination (PQE) for propositional CNF formulas. In contrast to full quantifier elimination, in PQE, one can limit the set of clauses taken out of the scope of quantifiers to a small subset of target clauses. The appeal of PQE is twofold. First, PQE can be dramatically simpler than full quantifier elimination. Second, it provides a language for performing incremental computations. Many verification problems (e.g. equivalence checking and model checking) are inherently incremental and so can be solved in terms of PQE. Our approach is based on deriving clauses depending only on unquantified variables that make the target clauses $\mathit{redundant}$. Proving redundancy of a target clause is done by construction of a ``certificate'' clause implying the former. We describe a PQE algorithm called $\mathit{START}$ that employs the approach above. We apply $\mathit{START}$ to generating properties of a design implementation that are not implied by specification. The existence of an $\mathit{unwanted}$ property means that this implementation is buggy. Our experiments with HWMCC-13 benchmarks suggest that $\mathit{START}$ can be used for generating properties of real-life designs

Formality and Informality in Cost-Benefit Analysis

Cost-benefit analysis (CBA) is usually treated as a monolith. In fact, the term can refer to a broad variety of decisionmaking practices, ranging from a qualitative comparison of pros and cons to a highly formalized and technical method grounded in economic theory that monetizes both costs and benefits, discounts to present net value, and locates the point at which the marginal benefits curve crosses the marginal costs curve. This article develops a typology that helps to conceptualize the multiple varieties of CBA along a formality-informality spectrum. It then uses this typology to analyze the treatment of CBA by the academic community and the three branches of the federal government. In academic and policy circles, the formal end of this spectrum generates far more controversy than the informal end. Additionally, the law (federal environmental statutes and case law) seems to favor informal over formal varieties of CBA. Nonetheless, the executive branch appears to be moving toward the formal end of the spectrum. Executive Orders and guidance documents direct agencies to conduct a highly formal mode of CBA. And anecdotal evidence suggests that agencies often go out of their way to give their CBAs the trappings of formality, sometimes in ways that lead to irrational results. I argue that 1) failing to distinguish between formal and informal CBA, and the many varieties in between, has led to muddled thinking and to misuses of CBA; and 2) the trend toward formality in the executive branch is out of step with Congress and the courts and may be counterproductive, where, for example, it leads to what I call “false formality”—a corruption of CBA that can occur when agencies fail to clearly and consistently define where on the formality-informality spectrum a particular CBA falls