Is behavioral integration a necessary feature of belief in folk psychology? Our data from over 5,000 people across 26 samples, spanning 22 countries suggests that it is not. Given the surprising cross-cultural robustness of our findings, we argue that the types of evidence for the ascription of a belief are, at least in some circumstances, lexicographically ordered: assertions are first taken into account, and when an agent sincerely asserts that p, nonlinguistic behavioral evidence is disregarded. In light of this, we (...) take ourselves to have discovered a universal principle governing the ascription of beliefs in folk psychology. (shrink)

Is behavioral integration (i.e., which occurs when a subjects assertion that p matches her non-verbal behavior) a necessary feature of belief in folk psychology? Our data from nearly 6,000 people across twenty-six samples, spanning twenty-two countries suggests that it is not. Given the surprising cross-cultural robustness of our findings, we suggest that the types of evidence for the ascription of a belief are, at least in some circumstances, lexicographically ordered: assertions are first taken into account, and when an agent sincerely (...) asserts that p, non-linguistic behavioral evidence is disregarded. In light of this, we take ourselves to have discovered a universal principle governing the ascription of beliefs in folk psychology. (shrink)

In his article "Reassurance via Translation" Marcel Crabbe proposed a formalism to obtain reassurance and classical recapture in the setting of minimal FDE. His formalism proved to be general enough to be extended in order to formalize other forms of non-monotonic systems based on preference relations. It is the aim of this article to show how his result can be extended in a natural way by combining two different reasoning systems, namely minimal FDE and circumscription, in order to get (...) a paraconsistent and paracomplete version of circumscription, which we will call paracomplistent circumscription, which has the advantages of FDE and circumscription but is neither explosive nor lacks modus ponens in consistent contexts. Furthermore, we will complete a proof Crabbe left unfinished. (shrink)

A conservative extension of first order logic, suitable for circumscriptive inference, is introduced.

The use of circumscription for formalizing commonsense knowledge and reasoning requires that a circumscription policy be selected for each particular application: we should specify which predicates are circumscribed, which predicates and functions are allowed to vary, and what priorities between the circumscribed predicates are established. The circumscription policy is usually described either informally or using suitable metamathematical notation. In this paper we propose a simple and general formalism which permits describing circumscription policies by axioms, included in (...) the knowledge base along with the axioms describing the objects of reasoning. The new formalism is illustrated by recasting some of the familiar applications of circumscription in its terms. (shrink)

SUMMARYSchleiermacher's doctrine of the Trinity is constituted not only by his Glaubenslehre but also in Über den Gegensatz zwischen der Sabellianischen und der Athanasianischen Vorstellung von der Trinität . Schleiermacher can be seen to construe the persons of the Trinity as the circumscription of divinity. This point leads to consideration of divine wisdom as the ground of both the immanent and economic Trinity.

We consider McCarthy's notions of predicate circumscription and formula circumscription. We show that the decision problems “does θ have a countably infinite minimal model” and “does φ hold in every countably infinite minimal model of θ” are complete Σ 1 2 and complete π 1 2 over the integers, for both forms of circumscription. The set of structures definable as first order definable subsets of countably infinite minimal models is the set of structures which are Δ 1 (...) 2 over the integers, for both forms of circumscription. Thus, restricted to countably infinite structures, predicate and formula circumscription define the same sets and have equally difficult decision problems. With general formula circumscription we can define several infinite cardinals, so the decidability problems are dependent upon the axioms of set theory. (shrink)

We investigate expressiveness and definability issues with respect to minimal models, particularly in the scope of Circumscription. First, we give a proof of the failure of the Löwenheim-Skolem Theorem for Circumscription. Then we show that, if the class of P; Z-minimal models of a first-order sentence is Δ-elementary, then it is elementary. That is, whenever the circumscription of a first-order sentence is equivalent to a first-order theory, then it is equivalent to a finitely axiomatizable one. This means (...) that classes of models of circumscribed theories are either elementary or not Δ-elementary. Finally, using the previous result, we prove that, whenever a relation Pi is defined in the class of P; Z-minimal models of a first-order sentence Φ and whenever such class of P; Z-minimal models is Δ-elementary, then there is an explicit definition ψ for Pi such that the class of P; Z-minimal models of Φ is the class of models of Φ ∧ ψ. In order words, the circumscription of P in Φ with Z varied can be replaced by Φ plus this explicit definition ψ for Pi. (shrink)

Since its inception in the work on fallacies of Charles Hamblin, formal dialectic has been the object of an unparalleled level of optimism concerning the potential of its analytical contribution to fallacy inquiry. This optimism has taken the form of a rapid proliferation of formal dialectical studies of arguments in general and fallacious arguments in particular under the auspices of theorists such as Jim Mackenzie and John Woods and Douglas Walton, to name but a few. Notwithstanding the interest in, and (...) the hopes for, a formal dialectical analysis of the fallacies, such an analysis, I will demonstrate subsequently, leads to much unintelligibility in fallacy inquiry. The context of my argument will be the philosophical views of Hilary Putnam, particularly Putnam's claim that when we theorise in relation to rationality, the unintelligibility of the conception of rationality to emerge from this theoretical process can be traced to the circumscription of rationality within this theoretical process. I charge formal dialectic with effecting a similar circumscription of argumentative rationality, a circumscription that, I will claim, is generative of unintelligibility in formal dialectical analyses of the fallacies. In this case, the context for my claims will be the formal dialectical analyses of Walton and Batten, Rescher, Hamblin, Mackenzie and Hintikka, primarily in relation to the petitio principii fallacy. My conclusion examines a number of the reasons, both historical and conceptual, which have made it seem that it is possible to fully circumscribe the notion of argumentative rationality. (shrink)

We propose an epistemic logic in which knowledge is fully introspective and implies truth, although truth need not imply epistemic possibility. The logic is presented in sequential format and is interpreted in a natural class of partial models, called balloon models. We examine the notions of honesty and circumscription in this logic: What is the state of an agent that only knows and which honest enable such circumscription? Redefining stable sets enables us to provide suitable syntactic and semantic (...) criteria for honesty. The rough syntactic definition of honesty is the existence of a minimal stable expansion, so the problem resides in the ordering relation underlying minimality. We discuss three different proposals for this ordering, together with their semantic counterparts, and show their effects on the induced notions of honesty. (shrink)

Recently we proposed a method of compiling prioritized circumscription into answer set programming. However, its encoding has the guess and check structure, where the candidates are generated by the guess program and the check is expressed by the inconsistency of the check program. In this paper, we present another method which compiles prioritized circumscription into a single general disjunctive program by means of integration of the guess and check programs. The answer sets of the transformed GDP yield models (...) of a given circumscription by emulating the inconsistency of the check program using integrity constraints. Thanks to our integration technique, the circumscriptive theorem prover to evaluate a query with respect to prioritized circumscription is easily established by expressing the inconsistency check in a single GDP. Our experimental results show that the performance of the tool we have implemented using our new method has not only improved remarkably, i.e. reduction of runtime as compared to our previous method, but has also exceeded that of the recently developed software tool, prio_circ2dlp, for prioritized circumscription as far as our experiments are concerned. (shrink)

We introduce a family of preferential logics that are useful for handling information with different levels of uncertainty. The corresponding consequence relations are nonmonotonic, paraconsistent, adaptive, and rational. It is also shown that the formalisms in this family can be embedded in corresponding four-valued logics with at most three uncertainty levels, and that reasoning with these logics can be simulated by algorithms for processing circumscriptive theories, such as DLS and SCAN.

We investigate induction from the viewpoint of nonmonotonic reasoning. Induction we consider in this paper is descriptive induction. Hypotheses from descriptive induction have the weak property that they only describe rules with respect to the observations and do not realize an inductive leap. In this paper, we define a new form of descriptive induction with circumscription and the idea of explanation and show two procedures for computing it. The new descriptive induction is called circumscriptive induction. By deciding the roles (...) of predicates in circumscription, we can intentionally minimize models of a given inductive problem. By adopting the idea of explanation, we can distinguish between background knowledge and observations. Additionally, we consider the relationship between the way of choosing the roles of predicates in computing circumscription and the property of hypotheses obtained by circumscriptive induction. It is shown that hypotheses from circumscriptive induction reflect a difference between background knowledge and observations and do not realize an inductive leap. We also investigate revision of hypotheses which is as important as generation of hypotheses. In a process of hypothesis revision, a difference between previous induction and circumscriptive induction is clearly characterised. (shrink)

In terms of Groenendijk and Stokhofs (1984) formalization of exhaustive interpretation, many conversational implicatures can be accounted for. In this paper we justify and generalize this approach. Our justification proceeds by relating their account via Halpern and Moses (1984) non-monotonic theory of only knowing to the Gricean maxims of Quality and the first sub-maxim of Quantity. The approach of Groenendijk and Stokhof (1984) is generalized such that it can also account for implicatures that are triggered in subclauses not entailed by (...) the whole complex sentence. (shrink)

The circumscription of taxa and classification of organisms are fundamental tasks in the systematization of biological diversity. Their success depends on a unified idea concerning the species concept, evolution, and taxonomy; paradoxically, however, it requires a complete distinction between taxa and evolutionary units. To justify this view, I discuss these three topics of systematics. Species concepts are examined, and I propose a redefinition for the Taxonomic Species Concept based on nomenclatural properties, in which species are classes conventionally represented by (...) a binomial. Speciation is subsequently discussed, to demonstrate that concepts on the evolutionary process are damaged when species are considered as evolutionary units. Speciation should be considered a transition among patterns of a population and, consequently, always a sympatric process. This view contrasts with the majority of speciation models, which analyze cladogeneses and classify speciation geographically, usually considering allopatry the essential condition for the differentiation process. Finally, taxonomy is considered, to show that the equivalence between evolutionary and taxonomic units may also damage the practice of biological systematization. Principles and rules of nomenclature and classification should offer freedom to accommodate divergent opinions about systematics and to incorporate the evolution of knowledge; therefore, they should remain independent of biological theories. (shrink)

3rd ed, 2021. A circumscription of the classical theory of computation building up from the Chomsky hierarchy. With the usual topics in formal language and automata theory.