A logic for reasoning about probabilities

We consider a language for reasoning about probability which allows us to make statements such as “the probability of E₁ is less than ” and “the probability of E₁ is at least twice the probability of E₂,” where E₁ and E₂ are arbitrary events. We consider the case where all events are measurable (i.e., represent measurable sets) and the more general case, which is also of interest in practice, where they may not be measurable. The measurable case is essentially a formalization of (the propositional fragment of) Nilsson's probabilistic logic. As we show elsewhere, the general (nonmeasurable) case corresponds precisely to replacing probability measures by Dempster-Shafer belief functions. In both cases, we provide a complete axiomatization and show that the problem of deciding satisfiability is NP-complete, no worse than that of propositional logic. As a tool for proving our complete axiomatizations, we give a complete axiomatization for reasoning about Boolean combinations of linear inequalities, which is of independent interest. This proof and others make crucial use of results from the theory of linear programming. We then extend the language to allow reasoning about conditional probability and show that the resulting logic is decidable and completely axiomatizable, by making use of the theory of real closed fields.     

A logic for reasoning about time and reliability

We present a logic for stating properties such as, after a request for service there is at least a 98% probability that the service will be carried out within 2 seconds. The logic extends the temporal logic CTL by Emerson, Clarke and Sistla with time and probabilities. Formulas are interpreted over discrete time Markov chains. We give algorithms for checking that a given Markov chain satisfies a formula in the logic. The algorithms require a polynomial number of arithmetic operations, in size of both the formula and the Markov chain. A simple example is included to illustrate the algorithms.This paper is a revised and extended version of a paper that has appeared under the title A Framework for Reasoning about Time and Reliability in the Proceeding of the 10 ^th IEEE Real-time Systems Symposium, Santa Monica CA, December 1989. The work presented here was performed while the authors were employed by the Swedish Institute of Computer Science (SICS), and partially supported by the Swedish Board for Technical Development (ESPRIT/BRA project 3096, SPEC) and the Swedish Telecommunication Administration (project: PROCOM).     

A functional logic for higher level reasoning about computation

In many areas of computation and reasoning, the value of an expression may depend on an implicit parameter, which may for example represent a program state, or time, or a possible world. In this paper we describe a formal first order logic which captures a general notion of expressions which depend on an implicit parameter. Both semantics and syntax are discussed. An important application of the logic, used as a running example, is to provide a basis for unifying the Hoare logic of procedural programs with the mathematically powerful techniques of classical logic and set theory. It is, however, beyond the scope of this paper to develop this application fully.     

A new modal logic for reasoning about space: spatial propositional neighborhood logic

It is widely accepted that spatial reasoning plays a central role in artificial intelligence, for it has a wide variety of potential applications, e.g., in robotics, geographical information systems, and medical analysis and diagnosis. While spatial reasoning has been extensively studied at the algebraic level, modal logics for spatial reasoning have received less attention in the literature. In this paper we propose a new modal logic, called spatial propositional neighborhood logic (SpPNL for short) for spatial reasoning through directional relations. We study the expressive power of SpPNL, we show that it is able to express meaningful spatial statements, we prove a representation theorem for abstract spatial frames, and we devise a (non-terminating) sound and complete tableaux-based deduction system for it. Finally, we compare SpPNL with the well-known algebraic spatial reasoning system called rectangle algebra.      

A logic for reasoning with inconsistency

Most known computational approaches to reasoning have problems when facing inconsistency, so they assume that a given logical system is consistent. Unfortunately, the latter is difficult to verify and very often is not true. It may happen that addition of data to a large system makes it inconsistent, and hence destroys the vast amount of meaningful information. We present a logic, called APC (annotated predicate calculus; cf. annotated logic programs of [4, 5]), that treats any set of clauses, either consistent or not, in a uniform way. In this logic, consequences of a contradiction are not nearly as damaging as in the standard predicate calculus, and meaningful information can still be extracted from an inconsistent set of formulae. APC has a resolution-based sound and complete proof procedure. We also introduce a novel notion of epistemic entailment and show its importance for investigating inconsistency in predicate calculus as well as its application to nonmonotonic reasoning. Most importantly, our claim that a logical theory is an adequate model of human perception of inconsistency, is actually backed by rigorous arguments.A preliminary report on this research appeared in LICS'89.Work of M. Kifer was supported in part by the NSF grants DCR-8603676, IRI-8903507.Work of E. L. Lozinskii was supported in part by Israel National Council for Research and Development under the grants 2454-3-87, 2545-2-87, 2545-3-89 and by Israel Academy of Science, grant 224-88.     

A propositional probabilistic logic with discrete linear time for reasoning about evidence

The aim of the paper is to present a sound, strongly complete and decidable probabilistic temporal logic that can model reasoning about evidence. The formal system developed here is actually a solution of a problem proposed by Halpern and Pucella (J Artif Intell Res 26:1–34, 2006).     

RGITL: A temporal logic framework for compositional reasoning about interleaved programs

This paper gives a self-contained presentation of the temporal logic Rely-Guarantee Interval Temporal Logic (RGITL). The logic is based on interval temporal logic (ITL) and higher-order logic. It extends ITL with explicit interleaved programs and recursive procedures. Deduction is based on the principles of symbolic execution and induction, known from the verification of sequential programs, which are transferred to a concurrent setting with temporal logic. We include an interleaving operator with compositional semantics. As a consequence, the calculus permits proving decomposition theorems which reduce reasoning about an interleaved program to reasoning about individual threads. A central instance of such theorems are rely-guarantee (RG) rules, which decompose global safety properties. We show how the correctness of such rules can be formally derived in the calculus. Decomposition theorems for other global properties are also derivable, as we show for the important progress property of lock-freedom. RGITL is implemented in the interactive verification environment KIV. It has been used to mechanize various proofs of concurrent algorithms, mainly in the area oflinearizable and lock-free algorithms.     

A logic programming system for nonmonotonic reasoning

The evolution of logic programming semantics has included the introduction of a new explicit form of negation, beside the older implicit (or default) negation typical of logic programming. The richer language has been shown adequate for a spate of knowledge representation and reasoning forms.The widespread use of such extended programs requires the definition of a correct top-down querying mechanism, much as for Prolog wrt. normal programs. One purpose of this paper is to present and exploit a SLDNF-like derivation procedure, SLX, for programs with explicit negation under well-founded semantics (WFSX) and prove its soundness and completeness. (Its soundness wrt. the answer-sets semantics is also shown.) Our choice ofWFSX as the base semantics is justi-fied by the structural properties it enjoys, which are paramount for top-down query evaluation.Of course, introducing explicit negation requires dealing with contradiction. Consequently, we allow for contradiction to appear, and show moreover how it can be removed by freely changing the truth-values of some subset of a set of predefined revisable literals. To achieve this, we introduce a paraconsistent version ofWFSX, WFSX _p , that allows contradictions and for which our SLX top-down procedure is proven correct as well.This procedure can be used to detect the existence of pairs of complementary literals inWESX _p simply by detecting the violation of integrity rulesf L, -L introduced for eachL in the language of the program. Furthermore, integrity constraints of a more general form are allowed, whose violation can likewise be detected by SLX.Removal of contradiction or integrity violation is accomplished by a variant of the SLX procedure that collects, in a formula, the alternative combinations of revisable literals' truth-values that ensure the said removal. The formulas, after simplification, can then be satisfied by a number of truth-values changes in the revisable, among true, false, and undefined. A notion of minimal change is defined as well that establishes a closeness relation between a program and its revisions. Forthwith, the changes can be enforced by introducing or deleting program rules for the revisable literals.To illustrate the usefulness and originality of our framework, we applied it to obtain a novel logic programming approach, and results, in declarative debugging and model-based diagnosis problems.     

On compositional reasoning about anonymity and privacy in epistemic logic

In this paper, we exploit epistemic logic (or the modal logic of knowledge) for multiagent systems to discuss the compositionality of several privacy-related information-hiding/disclosure properties. The properties considered here are anonymity, privacy, onymity, and identity. Our initial observation reveals that anonymity/privacy properties are not necessarily sequentially compositional. This means that even though a system comprising several sequential phases satisfies a certain unlinkability property in each phase, the entire system does not always enjoy a desired unlinkability property. We show that the compositionality can be guaranteed provided that the phases of the system satisfy what we call independence assumptions. More specifically, we develop a series of theoretical case studies of what assumptions are sufficient to guarantee the sequential compositionality of various degrees of anonymity, privacy, onymity, and/or identity properties. Similar results for parallel composition are also discussed. Further, we use the probabilistic extension of epistemic logic to consider the compositionality of probabilistic anonymity/privacy. We show that the compositionality can also be guaranteed in the probabilistic setting, provided that the phases of the system satisfy a probabilistic independence assumption.     

Modal logic for default reasoning

In the paper we introduce a variant of autoepistemic logic that is especially suitable for expressing default reasonings. It is based on the notion of iterative expansion. We show a new way of translating default theories into the language of modal logic under which default extensions correspond exactly to iterative expansions. Iterative expansions have some attractive properties. They are more restrictive than autoepistemic expansions, and, for some classes of theories, than moderately grounded expansions. At the same time iterative expansions avoid several undesirable properties of strongly grounded expansions, for example, they are grounded in the whole set of the agent's initial assumptions and do not depend on their syntactic representation.Iterative expansions are defined syntactically. We define a semantics which leads to yet another notion of expansion — weak iterative expansion — and we show that there is an important class of theories, that we call -programs, for which iterative and weak iterative expansions coincide. Thus, for -programs, iterative expansions can be equivalently defined by semantic means.This work was partially supported by Army Research Office under grant DAAL03-89-K-0124, and by National Science Foundation and the Commonwealth of Kentucky EPSCoR program under grant RII 8610671.     

基于逻辑推理的数字权利动态描述研究*

摘要：使用过程中数字权利的动态描述一直都是DRM应用系统研究的热点。提出一种基于逻辑推理的数字权利动态描述模型,在定义好该模型的基本要素以后,利用逻辑推理工具Prolog深入探讨和分析该模型中数字证书逻辑推理过程,并给出了相应的应用实例。     

A dynamic logic for privacy compliance

Knowledge based privacy policies are more declarative than traditional action based ones, because they specify only what is permitted or forbidden to know, and leave the derivation of the permitted actions to a security monitor. This inference problem is already non trivial with a static privacy policy, and becomes challenging when privacy policies can change over time. We therefore introduce a dynamic modal logic that permits not only to reason about permitted and forbidden knowledge to derive the permitted actions, but also to represent explicitly the declarative privacy policies together with their dynamics. The logic can be used to check both regulatory and behavioral compliance, respectively by checking that the permissions and obligations set up by the security monitor of an organization are not in conflict with the privacy policies, and by checking that these obligations are indeed enforced.     

A new generic scheme for functional logic programming with constraints

In this paper we propose a new generic scheme CFLP풟, intended as a logical and semantic framework for lazy Constraint Functional Logic Programming over a parametrically given constraint domain 풟. As in the case of the well known CLP풟 scheme for Constraint Logic Programming, 풟 is assumed to provide domain specific data values and constraints. CFLP풟 programs are presented as sets of constrained rewrite rules that define the behavior of possibly higher order and/or non-deterministic lazy functions over 풟. As a main novelty w.r.t. previous related work, we present a Constraint Rewriting Logic CRWL풟 which provides a declarative semantics for CFLP풟 programs. This logic relies on a new formalization of constraint domains and program interpretations, which allows a flexible combination of domain specific data values and user defined data constructors, as well as a functional view of constraints. This research has been partially supported by the Spanish National Projects MELODIAS (TIC2002-01167), MERIT-FORMS (TIN2005-09207-C03-03) and PROMESAS-CAM (S-0505/TIC/0407).     

LAR: A logic of algorithmic reasoning

Summary Reasoning about programs involves some logical framework which seems to go beyond classical predicate logic. LAR is an extension of predicate logic by additional concepts which are to formalize our natural reasoning about algorithms. Semantically, this extension introduces an underlying time scale on which formulas are considered and time shifting connectives. Besides a full model-theoretic treatment, a consistent and complete formal system for LAR is given. The pure logical system can serve as a basis for various theories. As an example, a theory of while program schemes is developed which contains Hoare's correctness proof system.     

Defeasible reasoning and logic programming

The general conditions of epistemic defeat are naturally represented through the interplay of two distinct kinds of entailment, deductive and defeasible. Many of the current approaches to modeling defeasible reasoning seek to define defeasible entailment via model-theoretic notions like truth and satisfiability, which, I argue, fails to capture this fundamental distinction between truthpreserving and justification-preserving entailments. I present an alternative account of defeasible entailment and show how logic programming offers a paradigm in which the distinction can be captured, allowing for the modeling of a larger range of types of defeat. This is possible through a natural extension of the declarative and procedural semantics of Horn clauses.     

A first-order logic for reasoning under uncertainty using rough sets

Reasoning with uncertain information is a problem of key importance when dealing with knowledge from real situations. Obtaining the precise numbers required by many uncertainty-handling formalisms can be a problem when building real systems. The theory of rough sets allows us to handle uncertainty without the need for precise numbers, and so has some advantages in such situations. The authors develop a set of symbolic truth values based upon rough sets which may be used to augment predicate logic, and provide methods for combining these truth values so that they may be propagated when augmented logic formulae are used in automated reasoning.