A logical expression of reasoning

A non-monotonic logic, the Logic of Plausible Reasoning (LPR), capable of coping with the demands of what we call complex reasoning, is introduced. It is argued that creative complex reasoning is the way of reasoning required in many instances of scientific thought, professional practice and common life decision taking. For managing the simultaneous consideration of multiple scenarios inherent in these activities, two new modalities, weak and strong plausibility, are introduced as part of the Logic of Plausible Deduction (LPD), a deductive logic specially designed to serve as the monotonic support for LPR. Axiomatics and semantics for LPD, together with a completeness proof, are provided. Once LPD has been given, LPR may be defined via a concept of extension over LPD. Although the construction of LPR extensions is first presented in standard style, for the sake of comparison with existing non-monotonic formalisms, alternative more elegant and intuitive ways for constructing non-monotonic LPR extensions are also given and proofs of their equivalence are presented.     

归纳接受与知识

归纳推理的结论进入知识集合的时候有一个“跳跃”的过程。根据什么规则接受归纳结论是归纳逻辑研究中的一个重要问题。概率接受规则与知识集合应当满足的一致性条件和演绎封闭条件之间存在着不协调,这种不协调性导致了抽彩悖论。该文介绍有代表性的归纳接受理论,指出归纳接受问题对归纳逻辑发展的影响。     

From Bayesian epistemology to inductive logic

Inductive logic admits a variety of semantics (Haenni et al. (2011) [7, Part 1]). This paper develops semantics based on the norms of Bayesian epistemology (Williamson, 2010 [16, Chapter 7]). Section 1 introduces the semantics and then, in Section 2, the paper explores methods for drawing inferences in the resulting logic and compares the methods of this paper with the methods of Barnett and Paris (2008) [2]. Section 3 then evaluates this Bayesian inductive logic in the light of four traditional critiques of inductive logic, arguing (i) that it is language independent in a key sense, (ii) that it admits connections with the Principle of Indifference but these connections do not lead to paradox, (iii) that it can capture the phenomenon of learning from experience, and (iv) that while the logic advocates scepticism with regard to some universal hypotheses, such scepticism is not problematic from the point of view of scientific theorising.     

Applied Logic without Psychologism

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance.     

Quantum Logic in Intuitionistic Perspective

In their seminal paper Birkhoff and von Neumann revealed the following dilemma:[ ] whereas for logicians the orthocomplementation properties of negation were the ones least able to withstand a critical analysis, the study of mechanics points to the distributive identities as the weakest link in the algebra of logic.In this paper we eliminate this dilemma, providing a way for maintaining both. Via the introduction of the "missing" disjunctions in the lattice of properties of a physical system while inheriting the meet as a conjunction we obtain a complete Heyting algebra of propositions on physical properties. In particular there is a bijective correspondence between property lattices and propositional lattices equipped with a so called operational resolution, an operation that exposes the properties on the level of the propositions. If the property lattice goes equipped with an orthocomplementation, then this bijective correspondence can be refined to one with propositional lattices equipped with an operational complementation, as such establishing the claim made above. Formally one rediscovers via physical and logical considerations as such respectively a specification and a refinement of the purely mathematical result by Bruns and Lakser (1970) on injective hulls of meet-semilattices. From our representation we can derive a truly intuitionistic functional implication on property lattices, as such confronting claims made in previous writings on the matter. We also make a detailed analysis of disjunctivity vs. distributivity and finitary vs. infinitary conjunctivity, we briefly review the Bruns-Lakser construction and indicate some questions which are left open.     

A verification framework for agent programming with declarative goals

A long and lasting problem in agent research has been to close the gap between agent logics and agent programming frameworks. The main reason for this problem of establishing a link between agent logics and agent programming frameworks is identified and explained by the fact that agent programming frameworks have hardly incorporated the concept of a declarative goal. Instead, such frameworks have focused mainly on plans or goals-to-do instead of the end goals to be realised which are also called goals-to-be. In this paper, the programming language GOAL is introduced which incorporates such declarative goals. The notion of a commitment strategy—one of the main theoretical insights due to agent logics, which explains the relation between beliefs and goals—is used to construct a computational semantics for GOAL. Finally, a proof theory for proving properties of GOAL agents is introduced. Thus, the main contribution of this paper, rather than the language GOAL itself, is that we offer a complete theory of agent programming in the sense that our theory provides both for a programming framework and a programming logic for such agents. An example program is proven correct by using this programming logic.     

An evolutionary system for neural logic networks using genetic programming and indirect encoding

Nowadays, intelligent connectionist systems such as artificial neural networks have been proved very powerful in a wide area of applications. Consequently, the ability to interpret their structure was always a desirable feature for experts. In this field, the neural logic networks (NLN) by their definition are able to represent complex human logic and provide knowledge discovery. However, under contemporary methodologies, the training of these networks may often result in non-comprehensible or poorly designed structures. In this work, we propose an evolutionary system that uses current advances in genetic programming that overcome these drawbacks and produces neural logic networks that can be arbitrarily connected and are easily interpretable into expert rules. To accomplish this task, we guide the genetic programming process using a context-free grammar and we encode indirectly the neural logic networks into the genetic programming individuals. We test the proposed system in two problems of medical diagnosis. Our results are examined both in terms of the solution interpretability that can lead in knowledge discovery, and in terms of the achieved accuracy. We draw conclusions about the effectiveness of the system and we propose further research directions.     

Extended Quantum Logic

The concept of quantum logic is extended so that it covers a more general set of propositions that involve non-trivial probabilities. This structure is shown to be embedded into a multi-modal framework, which has desirable logical properties such as an axiomatization, the finite model property and decidability.     

Low-literates’ support needs for societal participation learning: Empirical grounding of theory- and model-based design

Specialized learning support software can address the low societal participation of low-literate Dutch citizens. We use the situated Cognitive Engineering method to iteratively create a design specification for the envisioned system VESSEL: a Virtual Environment to Support the Societal participation Education of Low-literates. An initial high-level specification for this system is refined by incorporating the societal participation experiences of low-literate citizens into the design. In two series of user studies, the participant workshop and cultural probe methods were used with 23 low-literate participants. The Grounded Theory method was used to process the rich user data from these studies into the Societal Participation Experience of Low-Literates (SPELL) model. Using this experience model, the existing VESSEL specification was refined: requirements were empirically situated in the daily practice of low-literate societal participation, and new claims were written to explicate the learning effectiveness of the proposed VESSEL system. In conclusion, this study provides a comprehensive, theoretically and empirically grounded set of requirements and claims for the proposed VESSEL system, as well as the underlying SPELL model, which captures the societal participation experiences of low-literates citizens. The research methods used in this study are shown to be effective for requirements engineering with low-literate users.     

A First Order Nonmonotonic Extension of Constructive Logic

Certain extensions of Nelson's constructive logic N with strong negation have recently become important in arti.cial intelligence and nonmonotonic reasoning, since they yield a logical foundation for answer set programming (ASP). In this paper we look at some extensions of Nelson's .rst-order logic as a basis for de.ning nonmonotonic inference relations that underlie the answer set programming semantics. The extensions we consider are those based on 2-element, here-and-there Kripke frames. In particular, we prove completeness for .rst-order here-and-there logics, and their minimal strong negation extensions, for both constant and varying domains. We choose the constant domain version, which we denote by QN^c₅, as a basis for de.ning a .rst-order nonmonotonic extension called equilibrium logic. We establish several metatheoretic properties of QN^c₅, including Skolem forms and Herbrand theorems and Interpolation, and show that the .rst-oder version of equilibrium logic can be used as a foundation for answer set inference.     

Nonmonotonic abductive inductive learning

Inductive Logic Programming (ILP) is concerned with the task of generalising sets of positive and negative examples with respect to background knowledge expressed as logic programs. Negation as Failure (NAF) is a key feature of logic programming which provides a means for nonmonotonic commonsense reasoning under incomplete information. But, so far, most ILP research has been aimed at Horn programs which exclude NAF, and has failed to exploit the full potential of normal programs that allow NAF. By contrast, Abductive Logic Programming (ALP), a related task concerned with explaining observations with respect to a prior theory, has been well studied and applied in the context of normal logic programs. This paper shows how ALP can be used to provide a semantics and proof procedure for nonmonotonic ILP that utilises practical methods of language and search bias to reduce the search space. This is done by lifting an existing method called Hybrid Abductive Inductive Learning (HAIL) from Horn clauses to normal logic programs. To demonstrate its potential benefits, the resulting system, called XHAIL, is applied to a process modelling case study involving a nonmonotonic temporal Event Calculus (EC).     

Open answer set programming for the semantic web

We extend answer set programming (ASP) with, possibly infinite, open domains. Since this leads to undecidable reasoning, we restrict the syntax of programs, while carefully guarding knowledge representation mechanisms such as negation as failure and inequalities. Reasoning with the resulting extended forest logic programs (EFoLPs) can be reduced to finite answer set programming, for which reasoners are available.We argue that extended forest logic programming is a useful tool for uniformly representing and reasoning with both ontological and rule-based knowledge, as they can capture a large fragment of the OWL DL ontology language equipped with DL-safe rules. Furthermore, EFoLPs enable nonmonotonic reasoning, a desirable feature in locally closed subareas of the Semantic Web.     

中国逻辑史视野下的先秦易学与名辩学

19世纪以来的中国逻辑史研究,比照西方逻辑,仅仅将先秦的名辩学看成是中国逻辑史的主要部分。其间虽有对《周易》的涉及,但也是浅尝辄止。本文从《周易》经、传产生的年代,特别是《周易》经、传所蕴涵的逻辑内容与先秦名辩逻辑的代表人物孔子、惠施、邓析等人的思想对比,说明先秦易学逻辑对名辩逻辑产生了深刻的影响。得出《周易》的经、传发轫了中国古代逻辑中的推类理论,而名辩学尤其是墨家辩学的推类理论则是对自《周易》以来的推类逻辑传统的总结和提高的结论。     

A logic of comparative obligation

Normal systems of modal logic, interpreted as deontic logics, are unsuitable for a logic of conflicting obligations. By using modal operators based on a more complex semantics, however, we can provide for conflicting obligations, as in [9], which is formally similar to a fragment of the logic of ability later given in [2], Having gone that far, we may find it desirable to be able to express and consider claims about the comparative strengths, or degrees of urgency, of the conflicting obligations under which we stand. This paper, building on the formalism of the logic of ability in [2], provides a complete and decidable system for such a language.     

On the Algebraizability of Annotated Logics

Annotated logics were introduced by V.S. Subrahmanian as logical foundations for computer programming. One of the difficulties of these systems from the logical point of view is that they are not structural, i.e., their consequence relations are not closed under substitutions. In this paper we give systems of annotated logics that are equivalent to those of Subrahmanian in the sense that everything provable in one type of system has a translation that is provable in the other. Moreover these new systems are structural. We prove that these systems are weakly congruential, namely, they have an infinite system of congruence 1-formulas. Moreover, we prove that an annotated logic is algebraizable (i.e., it has a finite system of congruence formulas,) if and only if the lattice of annotation constants is finite.     

Hybrid Probabilistic Logic Programs as Residuated Logic Programs

In this paper we show the embedding of Hybrid Probabilistic Logic Programs into the rather general framework of Residuated Logic Programs, where the main results of (definite) logic programming are validly extrapolated, namely the extension of the immediate consequences operator of van Emden and Kowalski. The importance of this result is that for the first time a framework encompassing several quite distinct logic programming semantics is described, namely Generalized Annotated Logic Programs, Fuzzy Logic Programming, Hybrid Probabilistic Logic Programs, and Possibilistic Logic Programming. Moreover, the embedding provides a more general semantical structure paving the way for defining paraconsistent probabilistic reasoning with a logic programming semantics.     

Monotonicity in Practical Reasoning

Classic deductive logic entails that once a conclusion is sustained by a valid argument, the argument can never be invalidated, no matter how many new premises are added. This derived property of deductive reasoning is known as monotonicity. Monotonicity is thought to conflict with the defeasibility of reasoning in natural language, where the discovery of new information often leads us to reject conclusions that we once accepted. This perceived failure of monotonic reasoning to observe the defeasibility of natural-language arguments has led some philosophers to abandon deduction itself (!), often in favor of new, non-monotonic systems of inference known as `default logics'. But these radical logics (e.g., Ray Reiter's default logic) introduce their desired defeasibility at the expense of other, equally important intuitions about natural-language reasoning. And, as a matter of fact, if we recognize that monotonicity is a property of the form of a deductive argument and not its content (i.e., the claims in the premise(s) and conclusion), we can see how the common-sense notion of defeasibility can actually be captured by a purely deductive system.     

概率逻辑与模糊逻辑在精细化学习诊断中的对比研究

精细化学习诊断有助于客观准确探究学生学习现状,为实施有针对性的补救教学提供理论和数据支持。本文对比研究概率逻辑与模糊逻辑在精细化学习诊断中的表现。首先,从“概念”视角介绍和对比两种逻辑。其次,介绍两个分别基于上述两逻辑的代表性模型：HO-PINC和Fuzzy-DINA。然后,对比两模型在五个实证数据上表现。最后,通过模拟研究进一步对比两模型的心理计量学性能。DIC等模型-数据拟合指标和RMSE等参数返真性指标的结果表明两模型对同一批数据有较一致的分析结果。建议实践者忽略模型选择对数据分析的影响,从概念或思辨视角入手选择使用概率逻辑或模糊逻辑来定义属性。     

“Four-Valued” Semantics for the Relevant Logic R

This paper sets out two semantics for the relevant logic R based on Dunn's four-valued semantics for first-degree entailments. Unlike Routley's semantics for weak relevant logics, they do not use two ternary accessibility relations. Unlike Restall's semantics, they capture all of R. But there is a catch. Both of the present semantics are neighbourhood semantics, that is, they include sets of propositions in the specification of their frames.