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).     

Abductive reasoning in neural-symbolic systems

Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are interested in benefiting from developments made by each community. In particular, we are interested in the ability of non-symbolic systems (neural networks) to learn from experience using efficient algorithms and to perform massively parallel computations of alternative abductive explanations. At the same time, we would like to benefit from the rigour and semantic clarity of symbolic logic. We present two approaches to dealing with abduction in neural networks. One of them uses Connectionist Modal Logic and a translation of Horn clauses into modal clauses to come up with a neural network ensemble that computes abductive explanations in a top-down fashion. The other combines neural-symbolic systems and abductive logic programming and proposes a neural architecture which performs a more systematic, bottom-up computation of alternative abductive explanations. Both approaches employ standard neural network architectures which are already known to be highly effective in practical learning applications. Differently from previous work in the area, our aim is to promote the integration of reasoning and learning in a way that the neural network provides the machinery for cognitive computation, inductive learning and hypothetical reasoning, while logic provides the rigour and explanation capability to the systems, facilitating the interaction with the outside world. Although it is left as future work to determine whether the structure of one of the proposed approaches is more amenable to learning than the other, we hope to have contributed to the development of the area by approaching it from the perspective of symbolic and sub-symbolic integration.

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.     

Braine心理逻辑理论述评

该文对Braine提出的在推理心理学研究领域占居重要地位的“心理逻辑理论”做了综合述评。“心理逻辑理论”主要包括三方面内容:构成“心理逻辑理论”基础的一组推理规则图式、将推理规则图式应用于推理过程的推理方案、实际应用意义。Braine认为他和他的同事于1984年设计并实施的以“自然推理系统”所含各推理规则为实验材料的实验结果支持该理论的基本观点。     

Preferential theory revision

Employing a logic program approach, this paper focuses on applying preferential reasoning to theory revision, both by means of preferences among existing theory rules, and by means of preferences on the possible abductive extensions to the theory. And, in particular, how to prefer among plausible abductive explanations justifying observations.     

Reasoning about XML with temporal logics and automata

We show that problems arising in static analysis of XML specifications and transformations can be dealt with using techniques similar to those developed for static analysis of programs. Many properties of interest in the XML context are related to navigation, and can be formulated in temporal logics for trees. We choose a logic that admits a simple single-exponential translation into unranked tree automata, in the spirit of the classical LTL-to-Büchi automata translation. Automata arising from this translation have a number of additional properties; in particular, they are convenient for reasoning about unary node-selecting queries, which are important in the XML context. We give two applications of such reasoning: one deals with a classical XML problem of reasoning about navigation in the presence of schemas, and the other relates to verifying security properties of XML views.     

Termination of logic programs with imperfect information: applications and query procedure

A general logic programming framework allowing for the combination of several adjoint lattices of truth-values is presented. The language is sorted, enabling the combination of several reasoning forms in the same knowledge base. The contribution of the paper is two-fold: on the one hand, sufficient conditions guaranteeing termination of all queries for the fix-point semantics for a wide class of sorted multi-adjoint logic programs are presented and related to some well-known probability-based formalisms; in addition, we specify a general non-deterministic tabulation goal-oriented query procedure for sorted multi-adjoint logic programs over complete lattices. We prove its soundness and completeness as well as independence of the selection ordering. We apply the termination results to probabilistic and fuzzy logic programming languages, enabling the use of the tabulation proof procedure for query answering.     

Explaining the Past in the Geosciences

Abductive reasoning is central to reconstructing the past in the geosciences. This paper outlines the nature of the abductive method and restates it in Bayesian terms. Evidence plays a key role in this working method and, in particular, traces of the past are important in this explanatory framework. Traces, whether singularly or as groups, are interpreted within the context of the event for which they have evidential claims. Traces are not considered as independent entities but rather as inter-related pieces of information concerning the likelihood of specific events. Exemplification of the use of such traces is provided by dissecting an example of their use in the environmental reconstruction of mountain climate.     

Abductive inference in defeasible reasoning: a model for research programmes

Abduction is regarded as the inference process that goes from observations to explanations within a more general context or theoretical framework. There are good characterizations of abduction of surprising observations in monotonic theories. Also, in normal logic programs there are a tight relation among SLDNF and the abduction of negative literals. However, a problem that faces abduction is the explanation of anomalous observations, i.e., observations that are contradictory with respect to the current theory. For this reason, in this work we will consider the problem of embedding abduction of surprising and anomalous observations in defeasible (nonmonotonic) theories. We discuss some issues arising the pragmatic acceptance of abductive inferences in defeasible theories, and how to accommodate anomalous observations and characterize all the possible outcomes that a defeasible theory may face when confronted with new evidence. We explore the use of partial structures approach as a semantic foundation for our system. Finally, we discuss an application of our system as a formal device for representing the methodology of scientific research programmes. In this representation, a programme is regarded as a defeasible theory that draws predictions. When confronted with surprising or anomalous observations, the programme protects itself by means of heuristic procedures, which are represented in our system as abductive inference procedures.     

Variable Priorities and Exclusionary Reasons in Input/Output Logic

Jörg Hansen, John Horty, and Xavier Parent and Leendert van der Torre have all recently described some sort of nonmonotonic logic to model reasons and their interactions. Horty’s framework is broader in scope than the other two, encompassing both reasoning about the relative strengths of reasons and reasoning about which reasons to consider in the first place. Hansen discusses a plethora of approaches and examples, including Horty’s, arguing that his preferred system best captures our intuitions. And Parent and van der Torre present a family of systems of input/output logic, which are in some ways the most flexible. In this paper, I aim to combine these features. Without attempting to answer the question of which intuitions are the best to capture, I first argue that there are good reasons to explore systems that behave more like Hansen’s than Horty’s. I then show that Parent and van der Torre’s framework of input/output logic can exactly duplicate Hansen’s system but is flexible enough to produce other results as well. Finally, I extend their framework to include the additional kinds of reasoning Horty discusses, showing that the resulting theory can handle a wider range of cases than Horty’s.     

Naturalizing logic: Errors of reasoning vindicated: Logic reapproaches cognitive science

A complete revision of mainstream logic is an urgent task to be achieved. This revision will be able to bring logic into a creative rapprochement with cognitive science. This can be achieved by trying to do for logic what over forty years ago Quine and others attempted for epistemology. It is necessary to propose a “naturalization” of the logic of human inference. This paper deals with an examination of how the naturalization process might go, together with some indication of what might be achieved by it. To assist the reader in understanding the naturalization of logic I will take advantage of my own research on the concept of abduction, which vindicates the positive cognitive value of the fallacy of the affirming the consequent thanks to the so-called EC-model (Eco-Cognitive model), and of the recent book Errors of Reasoning: Naturalizing the Logic of Inference (2013) [86], by John Woods. While this paper certainly aims at promoting the research program on the naturalization of logic, it also further advocates the placement of abduction in the research programmes of logic, and stresses to what extent our contemporary philosophical and logical tradition is indebted towards Charles Sanders Peirce, a thinker often praised for his productivity but whose quality and importance are too often overlooked.     

Equivalence issues in abduction and induction

This paper discusses several equivalence issues in abduction and induction. Three different problems: equivalence of theories, equivalence of explanations, and equivalence of observations are considered in the context of first-order logic and nonmonotonic logic programming. Necessary and sufficient conditions for those problems, and computational complexity results are provided. These equivalence measures provide methods for comparing different abductive or inductive theories, and also state conditions for optimizing those theories in program development.     

Strategies in Syllogistic Reasoning

This paper is about syllogistic reasoning, i.e., reasoning from such pairs of premises as, All the chefs are musicians; some of the musicians are painters. We present a computer model that implements the latest account of syllogisms, which is based on the theory of mental models. We also report four experiments that were designed to test this account. Experiments 1 and 2 examined the strategies revealed by the participants' use of paper and pencil as aids to reasoning. Experiment 3 used a new technique to externalize thinking. The participants had to refute, if possible, putative conclusions by constructing external models that were examples of the premises but counterexamples of the conclusions. Experiment 4 used the same techniques to examine the participants' strategies as they drew their own conclusions from syllogistic premises. The results of the experiments showed that individuals not trained in logic can construct counterexamples, that they use similar operations to those implemented in the computer model, but that they rely on a much greater variety of interpretations of premises and of search strategies than the computer model does. We re-evaluates current theories of syllogistic reasoning in the light of these results.     

Rips的“证明心理学理论”述评

该文对Rips提出的“证明心理学理论”做了综合述评。这一理论主要包含三方面的内容:对推理过程与人类记忆相互关系的解释;(2)根据逻辑学中的“自然推理规则”进行修正后用于解释人类推理过程的推理规则;(3)关于如何控制推理过程的论述。Rips认为他于1983年设计并实施的以“自然推理系统”所含各推理规则为实验材料的实验结果支持该理论的基本观点。     

Foundations of Everyday Practical Reasoning

“Since today is Saturday, the grocery store is open today and will be closed tomorrow; so let’s go today”. That is an example of everyday practical reasoning—reasoning directly with the propositions that one believes but may not be fully certain of. Everyday practical reasoning is one of our most familiar kinds of decisions but, unfortunately, some foundational questions about it are largely ignored in the standard decision theory: (Q1) What are the decision rules in everyday practical reasoning that connect qualitative belief and desire to preference over acts? (Q2) What sort of logic should govern qualitative beliefs in everyday practical reasoning, and to what extent is that logic necessary for the purposes of qualitative decisions? (Q3) What kinds of qualitative decisions are always representable as results of everyday practical reasoning? (Q4) Under what circumstances do the results of everyday practical reasoning agree with the Bayesian ideal of expected utility maximization? This paper proposes a rigorous decision theory for answering all of those questions, which is developed in parallel to Savage’s (1954) foundation of expected utility maximization. In light of a new representation result, everyday practical reasoning provides a sound and complete method for a very wide class of qualitative decisions; and, to that end, qualitative beliefs must be allowed to be closed under classical logic plus a well-known nonmonotonic logic—the so-called system ?.     

逻辑训练对不同理性思维方式大学生三段论推理的影响

采用理性—经验思维方式量表对105名大学生进行测量,选出高、低理性思维方式各35名大学生进行实验,探讨了逻辑训练对不同理性思维方式大学生三段论推理的影响。结果表明：(1)高理性思维方式个体三段论推理的平均反应时快于低理性思维方式个体;非冲突类型题目推理的平均正确率高于冲突类型题目;逻辑训练可以提高个体三段论推理的平均反应时和正确率;(2)逻辑训练后非冲突任务类型题目的平均正确率高于冲突任务类型题目;(3)逻辑训练对低理性思维方式个体冲突任务类型题目平均正确率的提高效果更明显。这意味着逻辑训练可以显著提升个体的推理成绩,但不能完全消除信念偏差对推理的影响,而且逻辑训练对低理性思维方式个体推理成绩的提升效果更加明显。     

Balancing Social Responsibility and Personal Autonomy: Adolescents’ Reasoning About Community Service Programs

Many jurisdictions in North America have implemented mandatory community service programs in high schools. However, little research exists examining the reasoning of youth themselves about such programs. This study examined how youth reason about community service programs, and how they balance the prosocial goals of these programs against their personal autonomy. Seventy-two participants between 10 and 18 years old evaluated voluntary community service along with 4 hypothetical mandatory programs that varied according to whether students or the government decided the areas in which students would serve, and whether a structured reflection component was included. The findings reveal that youth are not simply self-focused but rather balance and coordinate considerations of autonomy and community in their judgments and reasoning about community service.     

The eco-cognitive model of abduction: Ἀπαγωγή now: Naturalizing the logic of abduction

Abduction (ἀπαγωγή, in ancient Greek, often translated as “leading away” or “reduction”) is a procedure in which something that lacks classical explanatory epistemic virtue can be accepted because it has virtue of another kind: Gabbay and Woods [15] contend (GW-schema) that abduction presents an ignorance-preserving or (ignorance-mitigating) character. From this perspective abductive reasoning is a response to an ignorance-problem; through abduction the basic ignorance – that does not have to be considered a total “ignorance” – is neither solved nor left intact. Abductive reasoning is an ignorance-preserving accommodation of the problem at hand. Is abduction really ignorance-preserving? To better answer this question I will introduce (and take advantage of) an eco-cognitive model (EC-Model) of abduction. It will be illustrated that through abduction, knowledge can be enhanced, even when abduction is not considered an inference to the best explanation in the classical sense of the expression, that is an inference necessarily characterized by an empirical evaluation phase, or an inductive phase, as Peirce called it. To further deepen the eco-cognitive character of abduction a simple genealogy of logic is provided: Aristotle clearly states that in syllogistic theory local/environmental cognitive factors – external to that peculiar inferential process, for example regarding users/reasoners, are given up. Indeed, to define syllogism Aristotle first of all insists that all syllogisms are valid and contends that the necessity of this kind of reasoning is related to the circumstance that “no further term from outside (ἔξωθɛν) is needed”, in sum syllogism is the fruit of a kind of eco-cognitive immunization. At the same time Aristotle presents a seminal perspective on abduction: the second part of the article considers the famous passage in Chapter B25 of Prior Analytics concerning ἀπαγωγή (“leading away”), also studied by Peirce. I contend that some of the current well-known distinctive characters of abductive cognition are already expressed, which are in tune with the EC-Model. By providing an illustration of the role of the method of analysis and of the middle terms in Plato's dialectic argumentation, considered as related to the diorismic/poristic process in ancient geometry – also, later on, emphasized by Proclus – I maintain that it is just this intellectual heritage which informs Aristotle' Chapter B25 on ἀπαγωγή. Even if, in general, Aristotle seems to sterilize, thanks to the invention of syllogistic theory, every “dialectic” background of reasoning, nevertheless in Chapter B25 he is still pointing to the fundamental inferential role in reasoning of those externalities that substantiate the process of “leading away” (ἀπαγωγή). Hence, we can gain a new positive perspective about the “constitutive” eco-cognitive character of abduction, just thanks to Aristotle himself. Finally, the paper presents an excursus on Aristotle's enthymemes from signs, disregarded by Peirce, but extremely important to stress the Aristotelian treatment of what I have called selective abduction. A forthcoming companion paper [35] will further deepen the EC-Model of abduction stressing stricter logical aspects: the first result will be that, contrarily to the classical logical view, relevance and plausibility in abductive reasoning have to be relativized and so the epistemologically embarrassing concepts of irrelevance and implausibility exculpated: they are not always offensive to reason.     

Logic and Social Cognition

This article takes off from Johan van Benthem’s ruminations on the interface between logic and cognitive science in his position paper “Logic and reasoning: Do the facts matter?”. When trying to answer Van Benthem’s question whether logic can be fruitfully combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social cognition, including attributions such as “Bob knows that Alice knows that he wrote a novel under pseudonym”. For intelligent interaction, it is important that the participants recursively model the mental states of other agents. Otherwise, an international negotiation may fail, even when it has potential for a win-win solution, and in a time-critical rescue mission, a software agent may depend on a teammate’s action that never materializes. First a survey is presented of past and current research on higher-order social cognition, from the various viewpoints of logic, artificial intelligence, and psychology. Do people actually reason about each other’s knowledge in the way proscribed by epistemic logic? And if not, how can logic and cognitive science productively work together to construct more realistic models of human reasoning about other minds? The paper ends with a delineation of possible avenues for future research, aiming to provide a better understanding of higher-order social reasoning. The methodology is based on a combination of experimental research, logic, computational cognitive models, and agent-based evolutionary models.     

Reasoning about partial functions with the aid of a computer

Partial functions are ubiquitous in both mathematics and computer science. Therefore, it is imperative that the underlying logical formalism for a general-purpose mechanized mathematics system provide strong support for reasoning about partial functions. Unfortunately, the common logical formalisms — first-order logic, type theory, and set theory — are usually only adequate for reasoning about partial functionsin theory. However, the approach to partial functions traditionally employed by mathematicians is quite adequatein practice. This paper shows how the traditional approach to partial functions can be formalized in a range of formalisms that includes first-order logic, simple type theory, and Von-Neumann—Bernays—Gödel set theory. It argues that these new formalisms allow one to directly reason about partial functions; are based on natural, well-understood, familiar principles; and can be effectively implemented in mechanized mathematics systems.Supported by the MITRE-Sponsored Research program. This paper is a written version (with references) of an address given at the Partial Functions and Programming: Foundational Questions conference held 17 February 1995 at the University ol California at Irvine.