It is shown that the constructive four-valued logic N4 can be faithfully embedded into the modal logic S4. This embedding is used to obtain complete, cut-free display sequent calculi for N4 and C4, the modal logic of consistency over N4. C4 is a natural monotonic base system for semantics-based non-monotonic reasoning.

Some interesting cases of non-monotonic reasoning have already been identified in medieval theological texts. Jacob Archambault proved in 2015 that the argumentation presented by St Anselm of Canterbury in his Proslogion has non-monotonic “embeddings”. My own contribution from 2011 indicated that we can argue that a non-monotonic logic underlies some discussions provided by St Thomas Aquinas in his Summa theologiae, and showed that Boethius of Dacia used non-monotonic reasoning in his De aeternitate mundi. In this article, I would like to (...) briefly present these examples and verify whether we can speak about similar cases in medieval Biblical exegesis. My aim is to outline particular problems connected with the identification of non- monotonicity which are specific to theology, as well as assumptions that should be adopted to successfully discuss this issue. (shrink)

With recent advancements in systems engineering and artificial intelligence, autonomous agents are increasingly being called upon to execute tasks that have normative relevance. These are tasks that directly—and potentially adversely—affect human well-being and demand of the agent a degree of normative-sensitivity and -compliance. Such norms and normative principles are typically of a social, legal, ethical, empathetic, or cultural nature. Whereas norms of this type are often framed in the abstract, or as high-level principles, addressing normative concerns in concrete applications of (...) autonomous agents requires the refinement of normative principles into explicitly formulated practical rules. This paper develops a process for deriving specification rules from a set of high-level norms, thereby bridging the gap between normative principles and operational practice. This enables autonomous agents to select and execute the most normatively favourable action in the intended context premised on a range of underlying relevant normative principles. In the translation and reduction of normative principles to SLEEC rules, we present an iterative process that uncovers normative principles, addresses SLEEC concerns, identifies and resolves SLEEC conflicts, and generates both preliminary and complex normatively-relevant rules, thereby guiding the development of autonomous agents and better positioning them as normatively SLEEC-sensitive or SLEEC-compliant. (shrink)

With recent advancements in systems engineering and artificial intelligence, autonomous agents are increasingly being called upon to execute tasks that have normative relevance. These are tasks that directly—and potentially adversely—affect human well-being and demand of the agent a degree of normative-sensitivity and -compliance. Such norms and normative principles are typically of a social, legal, ethical, empathetic, or cultural (‘SLEEC’) nature. Whereas norms of this type are often framed in the abstract, or as high-level principles, addressing normative concerns in concrete applications (...) of autonomous agents requires the refinement of normative principles into explicitly formulated practical rules. This paper develops a process for deriving specification rules from a set of high-level norms, thereby bridging the gap between normative principles and operational practice. This enables autonomous agents to select and execute the most normatively favourable action in the intended context premised on a range of underlying relevant normative principles. In the translation and reduction of normative principles to SLEEC rules, we present an iterative process that uncovers normative principles, addresses SLEEC concerns, identifies and resolves SLEEC conflicts, and generates both preliminary and complex normatively-relevant rules, thereby guiding the development of autonomous agents and better positioning them as normatively SLEEC-sensitive or SLEEC-compliant. (shrink)

This article presents results from a simulation‐based study of inheritance inference, that is, inference from the typicality of a property among a “base” class to its typicality among a subclass of the class. The study aims to ascertain which kinds of inheritance inferences are reliable, with attention to the dependence of their reliability upon the type of environment in which inferences are made. For example, the study addresses whether inheritance inference is reliable in the case of “exceptional subclasses” (i.e., subclasses (...) that are known to be atypical in some respect) and attends to variations in reliability that result from variations in the entropy level of the environment. A further goal of the study is to show that the reliability of inheritance inference depends crucially on which sorts of base classes are used in making inferences. One approach to inheritance inference treats the extension of any atomic predicate as a suitable base class. A second approach identifies suitable base classes with the cells of a partition (of a preselected size k) of the domain of objects that satisfies the condition of maximizing the similarity of objects that are assigned to the same class. In addition to permitting more inferences, our study shows that the second approach results in inheritance inferences that are far more reliable, particularly in the case of exceptional subclasses. (shrink)

The applicability of Bayesian conditionalization in setting one’s posterior probability for a proposition, α, is limited to cases where the value of a corresponding prior probability, PPRI(α|∧E), is available, where ∧E represents one’s complete body of evidence. In order to extend probability updating to cases where the prior probabilities needed for Bayesian conditionalization are unavailable, I introduce an inference schema, defeasible conditionalization, which allows one to update one’s personal probability in a proposition by conditioning on a proposition that represents a (...) proper subset of one’s complete body of evidence. While defeasible conditionalization has wider applicability than standard Bayesian conditionalization (since it may be used when the value of a relevant prior probability, PPRI(α|∧E), is unavailable), there are circumstances under which some instances of defeasible conditionalization are unreasonable. To address this difficulty, I outline the conditions under which instances of defeasible conditionalization are defeated. To conclude the article, I suggest that the prescriptions of direct inference and statistical induction can be encoded within the proposed system of probability updating, by the selection of intuitively reasonable prior probabilities. (shrink)

It is suggested that taking into account considerations that traditionally fall within the scope of computer science in general, and artificial intelligence in particular, sheds new light on the subject of causation. It is argued that adopting causal notions con be viewed as filling a computational need: They allow reasoning with incomplete information, facilitate economical representations, and afford relatively efficient methods for reasoning about those representations. Specifically, it is proposed that causal reasoning is intimately bound to nonmonotonic reasoning. An account (...) of causation is offered that relies upon this connection, and compares this proposal to previous accounts within philosophy and artificial intelligence. (shrink)

We identify two pragmatic problems in temporal reasoning, the qualification problem and the extended prediction problem, the latter subsuming the infamous frame problem. Solutions to those seem to call for nonmonotonic inferences, and yet naive use of standard nonmonotonic logics turns out to be inappropriate. Looking for an alternative, we first propose a uniform approach to constructing and understanding nonmonotonic logics. This framework subsumes many existing nonmonotonic formalisms, and yet is remarkably simple, adding almost no extra baggage to traditional logic. (...) We then use this framework to propose a solution to the qualification problem. We also outline a solution to the extended prediction problem, and speculate on a possible connection between the above discussion and the concept of causation. (shrink)

Systems of logico-probabilistic reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systems _O, P_, _Z_, and _QC_. These systems differ in the number of inferences they licence _. LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of drawing more false or uninformative conclusions. In the first part of the paper, we (...) present the four systems and extend each of them by theorems that allow one to compute almost-tight lower-probability-bounds for the conclusion of an inference, given lower-probability-bounds for its premises. In the second part of the paper, we investigate by means of computer simulations which of the four systems provides the best balance of reward versus risk. Our results suggest that system _Z_ offers the best balance. (shrink)

The basic theory of scientific understanding presented in Sections 1–2 exploits three main ideas.First, that to understand a phenomenonP (for a given agent) is to be able to fitP into the cognitive background corpusC (of the agent).Second, that to fitP intoC is to connectP with parts ofC (via arguments in a very broad sense) such that the unification ofC increases.Third, that the cognitive changes involved in unification can be treated as sequences of shifts of phenomena inC. How the theory fits (...) typical examples of understanding and how it excludes spurious unifications is explained in detail. Section 3 gives a formal description of the structure of cognitive corpuses which contain descriptive as well as inferential components. The theory of unification is then refined in the light of so called puzzling phenomena, to enable important distinctions, such as that between consonant and dissonant understanding. In Section 4, the refined theory is applied to several examples, among them a case study of the development of the atomic model. The final part contains a classification of kinds of understanding and a discussion of the relation between understanding and explanation. (shrink)

This essay seeks to give a contractarian foundation to the concept of Corporate Social Responsibility (CSR), meant as an extended model of corporate governance of the firm. Whereas, justificatory issues have been discussed in a related paper (Sacconi, L.: 2006b, this journal), in this essay I focus on the implementation of and compliance with this normative model. The theory of reputation games, with reference to the basic game of trust, is introduced in order to make sense of self-regulation as a (...) way to implement the social contract on the multi-fiduciary model of corporate governance. This affords understanding of why self-regulation, meant as mere recourse to a long-run strategy in a repeated trust game, fails. Two basic problems for the functioning of the reputation mechanism are examined: the cognitive fragility problem, and the motivational problem. As regards the cognitive fragilities of reputation (which result from the impact of unforeseen contingencies and from bounded rationality), the paper develops the logic and the structure that self-regulatory norms must satisfy if they are to serve as gap-filling tools with which to remedy cognitive limitations in the reputation mechanism. The motivation problem then arises from the possibility of sophisticated abuse by the firm. Developed in this case is an entirely new application of the theory of conformism-and-reciprocity-based preferences, the result of which is that the stakeholders refuse to acquiesce to sophisticated abuse on the part of the firm. (shrink)

This essay seeks to give a contractarian foundation to the concept of Corporate Social Responsibility, meant as an extended model of corporate governance of the firm. Whereas, justificatory issues have been discussed in a related paper, in this essay I focus on the implementation of and compliance with this normative model. The theory of reputation games, with reference to the basic game of trust, is introduced in order to make sense of self-regulation as a way to implement the social contract (...) on the multi-fiduciary model of corporate governance. This affords understanding of why self-regulation, meant as mere recourse to a long-run strategy in a repeated trust game, fails. Two basic problems for the functioning of the reputation mechanism are examined: the cognitive fragility problem, and the motivational problem. As regards the cognitive fragilities of reputation, the paper develops the logic and the structure that self-regulatory norms must satisfy if they are to serve as gap-filling tools with which to remedy cognitive limitations in the reputation mechanism. The motivation problem then arises from the possibility of sophisticated abuse by the firm. Developed in this case is an entirely new application of the theory of conformism-and-reciprocity-based preferences, the result of which is that the stakeholders refuse to acquiesce to sophisticated abuse on the part of the firm. (shrink)

We study the problem of embedding Halpern and Moses's modal logic of minimal knowledge states into two families of modal formalism for nonmonotonic reasoning, McDermott and Doyle's nonmonotonic modal logics and ground nonmonotonic modal logics. First, we prove that Halpern and Moses's logic can be embedded into all ground logics; moreover, the translation employed allows for establishing a lower bound (3p) for the problem of skeptical reasoning in all ground logics. Then, we show a translation of Halpern and Moses's logic (...) into a significant subset of McDermott and Doyle's formalisms. Such a translation both indicates the ability of Halpern and Moses's logic of expressing minimal knowledge states in a more compact way than McDermott and Doyle's logics, and allows for a comparison of the epistemological properties of such nonmonotonic modal formalisms. (shrink)

The history of science can be better understood against the background of a history of knowledge comprising not only theoretical but also intuitive and practical knowledge. This widening of scope necessitates a more concise definition of the concept of knowledge, relating its cognitive to its material and social dimensions. The history of knowledge comprises the history of institutions in which knowledge is produced and transmitted. This is an essential but hitherto neglected aspect of cultural evolution. Taking this aspect into account (...) one is led to the concept of extended evolution, which integrates the perspectives of niche construction and complex regulative networks. The paper illustrates this concept using four examples: the emergence of language, the Neolithic revolution, the invention of writing and the origin of mechanics. (shrink)

This article sketches a theory of objective probability focusing on nomic probability, which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the statistical syllogism. It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction (...) is not of the familiar Bayesian variety, but consists of a precise version of the traditional Nicod Principle and its statistical analogues. (shrink)

Probabilities are important in belief updating, but probabilistic reasoning does not subsume everything else (as the Bayesian would have it). On the contrary, Bayesian reasoning presupposes knowledge that cannot itself be obtained by Bayesian reasoning, making generic Bayesianism an incoherent theory of belief updating. Instead, it is indefinite probabilities that are of principal importance in belief updating. Knowledge of such indefinite probabilities is obtained by some form of statistical induction, and inferences to non-probabilistic conclusions are carried out in accordance with (...) the statistical syllogism. Such inferences have been the focus of much attention in the nonmonotonic reasoning literature, but the logical complexity of such inference has not been adequately appreciated. (shrink)

There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.

It is often assumed that cognitive science is built upon folk psychology, and that challenges to folk psychology are therefore challenges to cognitive science itself. We argue that, in practice, cognitive science and folk psychology treat entirely non-overlapping domains: cognitive science considers aspects of mental life which do not depend on general knowledge, whereas folk psychology considers aspects of mental life which do depend on general knowledge. We back up our argument on theoretical grounds, and also illustrate the separation between (...) cognitive scientific and folk psychological phenomena in a number of cognitive domains. We consider the methodological and theoretical significance of our arguments for cognitive science research. (shrink)

We discuss O&C's probabilistic approach from a probability logical point of view. Specifically, we comment on subjective probability, the indispensability of logic, the Ramsey test, the consequence relation, human nonmonotonic reasoning, intervals, generalized quantifiers, and rational analysis.

The paper provides a preliminary study of algebraic semantics for modal and superintuitionistic non-monotonic logics. The main question answered is: how can non-monotonic inference be understood algebraically?

This paper is an attempt to bring together two separated areas of research: classical mathematics and metamathematics on the one side, non-monotonic reasoning on the other. This is done by simulating nonmonotonic logic through antitonic theory extensions. In the first half, the specific extension procedure proposed here is motivated informally, partly in comparison with some well-known non-monotonic formalisms. Operators V and, more generally, U are obtained which have some plausibility when viewed as giving nonmonotonic theory extensions. In the second half, (...) these operators are treated from a mathematical and metamathematical point of view. Here an important role is played by U -closed theories and U -fixed points. The last section contains results on V-closed theories which are specific for V. (shrink)

Showing remarkable insight into the relationship between language and thought, Alan Turing in 1950 proposed the Imitation Game as a proxy for the question “Can machines think?” and its meaning and practicality have been debated hotly ever since. The Imitation Game has come under criticism within the Computer Science and Artificial Intelligence communities with leading scientists proposing alternatives, revisions, or even that the Game be abandoned entirely. Yet Turing’s imagined conversational fragments between human and machine are rich with complex instances (...) of inference of implied information, reasoning from generalizations, and meta-reasoning, challenges AI practitioners have wrestled with since at least 1980 and continue to study. We argue that the very fact the Imitation Game is so difficult may be the very reason it shouldn’t be changed or abandoned. The semi-decidability of the game at this point hints at the possibility of a hard limit to the powers of technology. (shrink)