Probability, Frequency and Reasonable Expectation.

Strategic games require reasoning about other people’s and one’s own beliefs or intentions. Although they have clear commonalities with psychological tests of theory of mind, they are not clearly related to theory of mind tests for children between 9 and 10 years of age “Flobbe et al. J Logic Language Inform 17(4):417–442 (2008)”. We studied children’s (5–12 years of age) individual differences in how they played a strategic game by analyzing the strategies that they applied in a zero, first, and (...) second-order reasoning task. For the zero-order task, we found two subgroups with different accuracy levels. For the first-order task, subgroups of children applied different suboptimal strategies or an optimal strategy. For the second-order task only suboptimal strategies were present. Strategy use for all tasks was related to age. The 5- and 6-year old children were additionally tested on theory of mind understanding and executive functioning. Strategy-use in these children was related to working memory, but not to theory of mind after correction for age, verbal ability and general IQ. (shrink)

This article traces the development of possible worlds semantics through the work of: Wittgenstein, 1913-1921; Feys, 1924; McKinsey, 1945; Carnap, 1945-1947; McKinsey, Tarski and Jónsson, 1947-1952; von Wright, 1951; Becker, 1952; Prior, 1953-1954; Montague, 1955; Meredith and Prior, 1956; Geach, 1960; Smiley, 1955-1957; Kanger, 1957; Hintikka, 1957; Guillaume, 1958; Binkley, 1958; Bayart, 1958-1959; Drake, 1959-1961; Kripke, 1958-1965.

This paper explores principles governing the rational balance among an agent's beliefs, goals, actions, and intentions. Such principles provide specifications for artificial agents, and approximate a theory of human action (as philosophers use the term). By making explicit the conditions under which an agent can drop his goals, i.e., by specifying how the agent is committed to his goals, the formalism captures a number of important properties of intention. Specifically, the formalism provides analyses for Bratman's three characteristic functional roles played (...) by intentions [7, 9], and shows how agents can avoid intending all the foreseen side-effects of what they actually intend. Finally, the analysis shows how intentions can be adopted relative to a background of relevant beliefs and other intentions or goals. By relativizing one agent's intentions in terms of beliefs about another agent's intentions (or beliefs'), we derive a preliminary account of interpersonal commitments. (shrink)

As Ruben notes, the macrostrategy can allow that the distinction may also be drawn at some micro level, but it insists that descent to the micro level is ...

In this paper we present BTC, which is a complete logic for branchingtime whose modal operator quantifies over histories and whose temporal operators involve a restricted quantification over histories in a given possible choice. This is a technical novelty, since the operators of the usual logics for branching-time such as CTL express an unrestricted quantification over histories and moments. The value of the apparatus we introduce is connected to those logics of agency that are interpreted on branching-time, as for instance (...) Stit Logics. (shrink)

Noam Chomsky's book on syntactic structures is a serious attempts on the part of a linguist to construct within the tradition of scientific theory-construction ...

The book from which these sections are excerpted is concerned with the prospects for assimilating the study of human intelligence and its products to the natural sciences through the investigation of cognitive structures, understood as systems of rules and representations that can be regarded as “mental organs.” These mental structui′es serve as the vehicles for the exercise of various capacities. They develop in the mind on the basis of an innate endowment that permits the growth of rich and highly articulated (...) structures along an intrinsically determined course under the triggering and partially shaping effect of experience, which fixes parameters in an intricate system of predetermined form. It is argued that the mind is modular in character, with a diversity of cognitive structures, each with its specific properties arid principles. Knowledge of language, of the behavior of objects, and much else crucially involves these mental structures, and is thus not characterizable in terms of capacities, dispositions, or practical abilities, nor is it necessarily grounded in experience in the standard sense of this term.Various types of knowledge and modes of knowledge acquisition are discussed in these terms. Some of the properties of the language faculty are investigated. The basic cognitive relation is “knowing a grammar”; knowledge of language is derivative and, correspondingly, raises further problems. Language as commonly understood is not a unitary phenomenon but involves a number of interacting systems: the “computational” system of grammar, which provides the representations of sound and meaning that permit a rich range of expressive potential, is distinct from a conceptual system with its own properties; knowledge of language must be distinguished from knowledge of how to use a language; and the various systems that enter into the knowledge and use of language must be further analyzed into their specific subcomponents. (shrink)

Chomsky proposes a reformulation of the theory of transformational generative grammar that takes recent developments in the descriptive analysis of particular ...

Recent theories of agency (sees to it that) of Nuel Belnap and Michael Perloff are examined, particularly in the context of an early proposal of the author.

In this article we strive to provide a detailed and principled analysis of the role of beliefs in goal processing—that is, the cognitive transition that leads from a mere desire to a proper intention. The resulting model of belief-based goal processing has also relevant consequences for the analysis of intentions, and constitutes the necessary core of a constructive theory of intentions, i.e. a framework that not only analyzes what an intention is, but also explains how it becomes what it is. (...) We discuss similarities and differences between our approach and other standard accounts of intention, in particular Bratman’s planning theory. The aim here is to question and refine the conceptual foundations of many theories of intentional action: as a consequence, although our analysis is not formal in itself, it is ultimately meant to have deep consequences for formal models of intentional agency. (shrink)

The Dappled World: A Study of the Boundaries of Science. nancy cartwright. Plato's Reception of Parmenides. john a. palmer.

This paper contains a formal treatment of the system of quantified epistemic logic sketched in Appendix II of Carlson (1983). Section 1 defines the syntax and recapitulates the model set rules and principles of the Appendix system. Section 2 defines a possible worlds semantics for this system, and shows that the Appendix system is complete with respect to this semantics. Section 3 extends the system by an explicit truth operatorT it is true that and considers quantification over nonexistent individuals. Section (...) 4 formalizes the idea of variable identity criteria typical of Hintikkian epistemic logic. (shrink)

Among the various meanings in which the word ‘probability’ is used in everyday language, in the discussion of scientists, and in the theories of probability, there are especially two which must be clearly distinguished. We shall use for them the terms ‘probability1’ and ‘probability2'. Probability1 is a logical concept, a certain logical relation between two sentences ; it is the same as the concept of degree of confirmation. I shall write briefly “c” for “degree of confirmation,” and “c” for “the (...) degree of confirmation of the hypothesis h on the evidence e“; the evidence is usually a report on the results of our observations. On the other hand, probability2 is an empirical concept; it is the relative frequency in the long run of one property with respect to another. The controversy between the so-called logical conception of probability, as represented e.g. by Keynes, and Jeffreys, and others, and the frequency conception, maintained e.g. by v. Mises and Reichenbach, seems to me futile. These two theories deal with two different probability concepts which are both of great importance for science. Therefore, the theories are not incompatible, but rather supplement each other. (shrink)

This is identical with the first edition (see 21: 2716) except for the addition of a Supplement containing 5 previously published articles and the bringing of the bibliography (now 73 items) up to date. The 5 added articles present clarifications or modifications of views expressed in the first edition. (PsycINFO Database Record (c) 2009 APA, all rights reserved).

In the current paper, we re-examine how abstract argumentation can be formulated in terms of labellings, and how the resulting theory can be applied in the field of modal logic. In particular, we are able to express the (complete) extensions of an argumentation framework as models of a set of modal logic formulas that represents the argumentation framework. Using this approach, it becomes possible to define the grounded extension in terms of modal logic entailment.

There are schools of logicians who claim that an argument is not valid unless the conclusion is relevant to the premises. In particular, relevance logicians reject the classical theses that anything follows from a contradiction and that a logical truth follows from everything. This chapter critically evaluates several different motivations for relevance logic, and several systems of relevance logic, finding them all wanting.

I am interested in extending modal calculi by adding propositional quantifiers, given by the rules for quantifier introduction: provided that p does not occur free in A.

Artificial intelligence research has foundered on the issue of representation. When intelligence is approached in an incremental manner, with strict reliance on interfacing to the real world through perception and action, reliance on representation disappears. In this paper we outline our approach to incrementally building complete intelligent Creatures. The fundamental decomposition of the intelligent system is not into independent information processing units which must interface with each other via representations. Instead, the intelligent system is decomposed into independent and parallel activity (...) producers which all interface directly to the world through perception and action, rather than interface to each other particularly much. The notions of central and peripheral systems evaporateeverything is both central and peripheral. Based on these principles we have built a very successful series of mobile robots which operate without supervision as Creatures in standard office environments. (shrink)

We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced (...) to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a "virtual" manner, using uniterated revision. (shrink)

We study belief change in the branching-time structures introduced in Bonanno (Artif Intell 171:144–160, 2007 ). First, we identify a property of branching-time frames that is equivalent (when the set of states is finite) to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies the AGM postulates. Second, we (...) provide a set of modal axioms that characterize the class of AGM-consistent frames within the modal logic introduced in Bonanno (Artif Intell 171:144–160, 2007 ). Third, we introduce a generalization of AGM belief revision functions that allows a clear statement of principles of iterated belief revision and discuss iterated revision both semantically and syntactically. (shrink)

Since belief revision deals with the interaction of belief and information over time, branching-time temporal logic seems a natural setting for a theory of belief change. We propose two extensions of a modal logic that, besides the next-time temporal operator, contains a belief operator and an information operator. The first logic is shown to provide an axiomatic characterization of the first six postulates of the AGM theory of belief revision, while the second, stronger, logic provides an axiomatic characterization of the (...) full set of AGM postulates. © 2006 Elsevier B.V. All rights reserved. (shrink)

In this paper, we investigate the use of event models for automated planning. Event models are the action defining structures used to define a semantics for dynamic epistemic logic. Using event models, two issues in planning can be addressed: Partial observability of the environment and knowledge. In planning, partial observability gives rise to an uncertainty about the world. For single-agent domains, this uncertainty can come from incomplete knowledge of the starting situation and from the nondeterminism of actions. In multi-agent domains, (...) an additional uncertainty arises from the fact that other agents can act in the world, causing changes that are not instigated by the agent itself. For an agent to successfully construct and execute plans in an uncertain environment, the most widely used formalism in the literature on automated planning is “belief states”: sets of different alternatives for the current state of the world. Epistemic logic is a significantly more expressive and theoretically better founded method for representing knowledge and ignorance about the world. Further, epistemic logic allows for planning according to the knowledge (and iterated knowledge) of other agents, allowing the specification of a more complex class of planning domains, than those simply concerned with simple facts about the world. We show how to model multi-agent planning problems using Kripke-models for representing world states, and event models for representing actions. Our mechanism makes use of slight modifications to these concepts, in order to model the internal view of agents, rather than that of an external observer. We define a type of planning domain called epistemic planning domains, a generalisation of classical planning domains, and show how epistemic planning can successfully deal with partial observability, nondeterminism, knowledge and multiple agents. Finally, we show epistemic planning to be decidable in the single-agent case, but only semi-decidable in the multi-agent case. (shrink)

There is a gap between two different modes of computation: the symbolic mode and the subsymbolic (neuron-like) mode. The aim of this paper is to overcome this gap by viewing symbolism as a high-level description of the properties of (a class of) neural networks. Combining methods of algebraic semantics and non-monotonic logic, the possibility of integrating both modes of viewing cognition is demonstrated. The main results are (a) that certain activities of connectionist networks can be interpreted as non-monotonic inferences, and (...) (b) that there is a strict correspondence between the coding of knowledge in Hopfield networks and the knowledge representation in weight-annotated Poole systems. These results show the usefulness of non-monotonic logic as a descriptive and analytic tool for analyzing emerging properties of connectionist networks. Assuming an exponential development of the weight function, the present account relates to optimality theory – a general framework that aims to integrate insights from symbolism and connectionism. The paper concludes with some speculations about extending the present ideas. (shrink)

This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.

Relevance logics are known to be sound and complete for relational semantics with a ternary accessibility relation. This paper investigates the problem of adequacy with respect to special kinds of dynamic semantics (i.e., proper relation algebras and relevant families of relations). We prove several soundness results here. We also prove the completeness of a certain positive fragment of R as well as of the first-degree fragment of relevance logics. These results show that some core ideas are shared between relevance logics (...) and relation algebras. Some details of certain incompleteness results, however, pinpoint where relevance logics and relation algebras diverge. To carry out these semantic investigations, we define a new tableaux formalization and new sequent calculi (with the single cut rule admissible) for various relevance logics. (shrink)

We consider two topological interpretations of the modal diamond—as the closure operator (C-semantics) and as the derived set operator (d-semantics). We call the logics arising from these interpretations C-logics and d-logics, respectively. We axiomatize a number of subclasses of the class of nodec spaces with respect to both semantics, and characterize exactly which of these classes are modally definable. It is demonstrated that the d-semantics is more expressive than the C-semantics. In particular, we show that the d-logics of the six (...) classes of spaces considered in the paper are pairwise distinct, while the C-logics of some of them coincide. (shrink)

We prove that S4 is complete with respect to Boolean combinations of countable unions of convex subsets of the real line, thus strengthening a 1944 result of McKinsey and Tarski 45 141). We also prove that the same result holds for the bimodal system S4+S5+C, which is a strengthening of a 1999 result of Shehtman 369).

We prove that S4 is complete with respect to Boolean combinations of countable unions of convex subsets of the real line, thus strengthening a 1944 result of McKinsey and Tarski 45 141). We also prove that the same result holds for the bimodal system S4+S5+C, which is a strengthening of a 1999 result of Shehtman 369).

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion ${\bf S4}\oplus {\bf S4}$ . We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies. We prove that both of these logics are complete for the product of rational numbers ${\Bbb Q}\times {\Bbb Q}$ (...) with the appropriate topologies. (shrink)

Taking Backward Induction as its running example, this paper explores avenues for a logic of information-driven social action. We use recent results on limit phenomena in knowledge updating and belief revision, procedural rationality, and a ‘Theory of Play’ analyzing how games are played by different agents.

Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic (...) logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods. (shrink)

Provability logic GLP is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of GLP interprets modalities as derivative operators of a polytopological space. Such spaces are called GLP-spaces whenever they satisfy all the axioms of GLP. We develop some constructions to build nontrivial GLP-spaces and show that GLP is complete w.r.t. the class of all GLP-spaces.