John S. Schlipf

• University of Cincinnati

We describe a novel formalism representing a system of chemical reactions, with imprecise rates of reactions and concentrations of chemicals, and describe a model reduction method, pruning, based on the chemical properties. We present two algorithms, midpoint approximation and interval approximation, for construction of efficient model abstractions...

A theoretical formalism is created for automated construction of gene regulatory relationships from noisy gene expression data. The formalism is able to express real valued queries. Stochastic variants of the formalism are used for automated abstractions of regulatory relationships to address nondeterminism and noise in the data. Computational feas...

First Order ID-Logic interprets general first order, non- monotone, inductive definability by generalizing the well- founded semantics for logic programs. We show that, for general (thus perhaps infinite) structures, inference in First Order ID-Logic is complete 1 2 over the natural numbers. We also prove a Skolem Theorem for the logic: every consi...

We identify a new relationship between classical and non- monotonic logic; specifically, we relate autarkies for CNF formulas (Monien and Speckenmeier) to unfounded sets for logic normal logic programs (Van Gelder, Ross, Schlipf). Using a natural way to construct a logic program PC from a CNF formula C, we show that that the all-negative autarkies...

Without Abstract

We introduce new approaches intended to speed up determining the satisabilit y of a given Boolean formula ' expressed as a conjunction of Boolean functions. A common practice in such cases, when using constraint-oriented methods, is to represent the functions as BDDs, then repeatedly cluster BDDs containing one or more variables, and nally existent...

A conflict clause represents a backtracking solver's analysis of why a conflict occurred. This analysis can be used to further prune the search space and to direct the search heuristic. The use of such clauses has been very important in improving the efficiency of satisfiability (SAT) solvers over the past few years, especially on structured proble...

Recent work has shown the value of using propositional SAT solvers, as opposed to pure BDD solvers, for solving many real-world Boolean Satisfiability prob- lems including Bounded Model Checking problems (BMC). We propose a SAT solver paradigm which combines the use of BDDs and search methods to support efficient implementation of complex search he...

We present a new approach to SAT solvers, supporting efficient implementation of highly sophisticated search heuristics over a range of propositional inputs, including CNF formulas, but particularly sets of arbitrary boolean constraints, represented as BDDs. The approach preprocesses the BDDs into state machines to allow for fast inferences based u...

Many state-of-the-art reconfigurable computers consist of multiple field-programmable processors connected through a programmable interconnect fabric. Interconnect synthesis is the process of configuring the interconnection network to match the communication requirements of the designs implemented on the processors. We formulate interconnect synthe...

this paper is in questions of decidability and tractability for open domain specifications -- open domain specifications using the finite open domain and arbitrarily large open domain hypotheses. For some corresponding results for the infinite open domain assumption we refer the reader to our paper [19]

We empirically studied the behavior of the 3-Valued Kripke-Kleene semantics in a parameterized distribution of random propositional logic programs. In our distribution, programs with m rules are generated from n propositional letters by repeating the following process m times: uniformly, randomly, and independently choose k letters (with replacemen...

We empirically investigated the difficulty of finding stable models for logic programs using backtracking, by trying to identify what makes random instances easy or hard. Additionally, we empirically investigated the effectiveness of the 4‐valued Kripke–Kleene semantics (4KK) and the 4‐valued well‐founded semantics (4WF) in the Niemelä and Simons’...

Heusch introduced the notion of pure implicational formulas. He showed that the falsifiability problem for pure implicational formulas with k negations is solvable in time O(n k ). Such falsifiability results are easily transformed to satisfiability results on CNF formulas. We show that the falsifiability problem for pure implicational formulas is...

A general logic program (abbreviated to "program" hereafter) is a set of rules that have both positive and negative subgoals. It is common to view a deductive database as a general logic program consisting of rules (IDB) sitting above elementary relations (EDB, facts). It is desirable to associate one Herbrand model with a program and think of that...

Limiting the number of times a variable appears in either the head or the body of a rule, we identify two classes of normal propositional logic programs. These classes have the desirable property that stable models, if they exist, can be found in linear time (worst case). We also identify a related class containing;programs for which the well-found...

We address methods of speeding up the calculation of the well-founded semantics for normal propositional logic programs. We first consider two algorithms already reported in the literature and show that these, plus a variation upon them, have much improved worst-case behavior for special cases of input. Then we propose a general algorithm to speed...

This paper surveys complexity, degree of uncomputability, and expressive power results for logic programming. Some major decision problem complexity results and other results for logic programming are also covered. It also proves several new results filling in previous gaps in the literature. The paper considers seven logic programming semantics: t...

We study the expressive of two semantics far deductive databases and logic programming: the well-founded semantics and the stable semantics. We compare them especially to two older semantics, the two-valued and three-valued program completion semantics. We identify the expressive power of the stable semantics and, in fairly general circumstances, t...

If a Horn set I has a single satisfying truth assignment or model then that model is said to be unique for I. The question of determining whether a unique model exists for a given Horn set I is shown to be solved in O(ff(L) L) time, where L is the sum of the lengths of the clauses in I and ff is the inverse Ackermann function. It is also shown that...

This paper completes an investigation of the logical expressibility of finite, locally stratified, general logic programs. We show that every hyperarithmetic set can be defined by a suitably chosen locally stratified logic program (as a set of values of a predicate over its perfect model). This is an optimal result, since the perfect model of a loc...

We present a simple quadratic-time algorithm for solving the satisfiability problem for a special class of boolean formulas. This class properly contains the class of extended Horn formulas and balanced formulas. Previous algorithms for these classes require testing membership in the classes. However, the problem of recognizing balanced formulas is...

When logic programming was generalized to allow negative subgoals, difficulties immediately arose concerning the meaning of negation as failure in the context of these subgoals. Various semantics have been proposed, each attempting to capture natural intuitions about negation as failure and to preserve other intuitive properties. We discuss several...

Various semantics for logic programs with negation are described in terms of a dualized program together with additional axioms, some of which are second-order formulas. The semantics of Clark, Fitting, and Kunen are characterized in this framework, and a finite first-order presentation of Kunen's semantics is described. A new axiom to represent “c...

Much research in the last few years has centered upon an idea called negation as failure. The basic idea of negation as failure is that, if an atomic "fact" (atomic sentence) is true, it must be demonstrably true - so if we cannot demonstrate that the atomic sentence is true, we should infer it to be false. Negation as failure clearly is not logica...

We compare the expressive powers of three semantics for deductive databases and logic programming: the 3-valued program completion semantics, the well-founded semantics, and the stable semantics, We identify the expressive power of the stable semantics, and in fairly general circumstances that of the well-founded semantics. Over infinite Herbrand m...

A general logic program (abbreviated to “program” hereafter) is a set of rules that have both positive and negative subgoals. It is common to view a deductive database as a general logic program consisting of rules (IDB) sitting above elementary relations (EDB, facts). It is desirable to associate one Herbrand model with a program and think of that...

We consider McCarthy's notions of predicate circumscription and formula circumscription. We show that the decision problems “does θ have a countably infinite minimal model” and “does φ hold in every countably infinite minimal model of θ” are complete and complete over the integers, for both forms of circumscription. The set of structures definable...

This paper is concerned with methods of reducing variability and computer time in a simulation study. The Monte Carlo swindle, through mathematical manipulations, has been shown to yield more precise estimates than the “naive” approach. In this study computer time is considered in conjunction with the variance estimates. It is shown that by this me...

We determine when a model M of ZF can be expanded to a model y of a weak extension of Gödel Bernays: GB + the ∆11 comprehension axiom. For nonstandard M, the ordinal of the standard part of M must equal the inductive closure ordinal of M, and M must satisfy the axioms of ZF with replacement and separation for formulas involving predicates for all h...

We determine when a model M \mathfrak {M} of ZF can be expanded to a model ⟨ M , X ⟩ \langle \mathfrak {M},\mathfrak {X}\rangle of a weak extension of Gödel Bernays: GB + {\text {GB}} + the Δ 1 1 \Delta _1^1 comprehension axiom. For nonstandard M \mathfrak {M} , the ordinal of the standard part of M \mathfrak {M} must equal the inductive closure or...

One of the most significant by-products of the study of admissible sets with urelements is the emphasis it has given to recursively saturated models. As suggested in [Schlipf, 1977], countable recursively saturated models (for finite languages) possess many of the desirable properties of saturated and special models. The notion of resplendency was...

Moschovakis generalized a theorem of Kleene to prove that if X is a collection of subsets of any acceptable structure m such that (m, K) ⊫ Δ11 comprehension, every hyperelementary subset of m is in k. We prove an analogous result for arbitrary m. We also get analogous results for m with an extra quantifier Q.

Moschovakis generalized a theorem of Kleene to prove that if X \mathfrak {X} is a collection of subsets of any acceptable structure M \mathfrak {M} such that ( M , X ) ⊨ Δ 1 1 (\mathfrak {M},\mathfrak {X}) \vDash \Delta _1^1 comprehension, every hyperelementary subset of M \mathfrak {M} is in X \mathfrak {X} . We prove an analogous result for arbit...

The notion of the next admissible set has proved to be a very useful notion in definability theory and generalized recursion theory, a unifying notion that has produced further interesting results in its own right. The basic treatment of the next admissible set above a structure ℳ of urelements is to be found in Barwise's [75] book Admissible sets...

The notions of recursively saturated and resplendent models grew out of the study of admissible sets with urelements and admissible fragments of L ω1ω , but, when applied to ordinary first order model theory, give us new tools for research and exposition. We will discuss their history in §3. The notion of saturated model has proven to be important...

Thesis (Ph. D.)--University of Wisconsin--Madison, 1975. Vita. Typescript. Includes bibliographical references.