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)

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)

The thesis tries to define and explain the rudiments of a 'nonphilosophical' or 'non-decisional' theory of materialism on the basis of a theoretical framework provided by the 'non-philosophy' of Francois Laruelle. Neither anti-philosophical nor anti-materialist in character, non-materialism tries to construct a rigorously transcendental theory of matter by using certain instances of philosophical materialism as its source material. The materialist decision to identify the real with matter is seen to retain a structural isomorphy with the phenomenological decision to identify the (...) real with the phenomenon. Both decisions are shown to operate on the basis of a methodological idealism; materialism on account of its confusion of matter and concept; phenomenology by virtue of its confusion of phenomenon and logos. By dissolving the respectively 'materiological' and 'phenomenological' amlphibolies which are the result of the failure to effect a rigorously transcendental separation between matter and concept on the one hand; and between phenomenon and logos on the other, non-materialist theory proposes to mobilise the non-hybrid or non-decisional concepts of a 'matter-without-concept' and of a 'phenomenon-without-logos' in order to effect a unified but non-unitary theory of phenomenology and materialism. The result is a materialisation of thinking that operates according to matter's foreclosure to decision. That is to say, a transcendental theory of the phenomenon that licenses limitless phenomenological plasticity, unconstrained by the apparatus of eidetic intuition or any horizon of apophantic disclosure; yet one which is simultaneously a transcendental theory of matter, uncontaminated by the bounds of empirical perception and free of all phenomenological circumscription. (shrink)

There are several areas in logic where the monotonicity of the consequence relation fails to hold. Roughly these are the traditional non-monotonic systems arising in Artificial Intelligence (such as defeasible logics, circumscription, defaults, ete), numerical non-monotonic systems (probabilistic systems, fuzzy logics, belief functions), resource logics (also called substructural logics such as relevance logic, linear logic, Lambek calculus), and the logic of theory change (also called belief revision, see Alchourron, Gärdenfors, Makinson [2224]). We are seeking a common axiomatic and semantical approach (...) to the notion of consequence whieh can be specialised to any of the above areas. This paper introduces the notions of structured consequence relation, shift operators and structural connectives, and shows an intrinsic connection between the above areas. (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.

Most of the work in default logic is about default theories that are completely specified. In this category are the proposals of appropriate semantics for default logic, the characterizations of the complexity of reasoning with a default theory, the algorithms for finding consequences of default theories, etc. Relatively little attention has been paid to the process of building a default theory, and most of the work on this topic is about translating knowledge bases from other formalisms (such as (...) circumscription, autoepistemic logic, and action description languages) into default logic. This paper is about expressing knowledge in default logic. In particular, we assume that defaults are initially formulated as normal, and are then corrected using specific inference examples. (shrink)

We present an approach to database update as a form of non monotonic temporal reasoning, the main idea of which is the (circumscriptive) minimization of changes with respect to a set of facts declared “persistent by default”. The focus of the paper is on the relation between this approach and the update semantics recently proposed by Katsuno and Mendelzon. Our contribution in this regard is twofold:We prove a representation theorem for KM semantics in terms of a restricted subfamily of (...) the operators defined by our construction.We show how the KM semantics can be generalized by relaxing our construction in a number of ways, each justified in certain intuitive circumstances and each corresponding to one specific postulate. It follows that there are reasonable update operators outside the KM family.Our approach is not dependent for its plausibility on this connection with KM semantics. Rather, it provides a relatively rich and flexible framework in which the frame and ramification problems can be solved in a systematic way by reasoning about default persistence of facts. (shrink)

We present an approach to database update as a form of non monotonic temporal reasoning, the main idea of which is the (circumscriptive) minimization of changes with respect to a set of facts declared persistent by default. The focus of the paper is on the relation between this approach and the update semantics recently proposed by Katsuno and Mendelzon. Our contribution in this regard is twofold: • We prove a representation theorem for KM semantics in terms of a restricted (...) subfamily of the operators defined by our construction. • We show how the KM semantics can be generalized by relaxing our construction in a number of ways, each justified in certain intuitive circumstances and each corresponding to one specific postulate. It follows that there are reasonable update operators outside the KM family. • Our approach is not dependent for its plausibility on this connection with KM semantics. Rather, it provides a relatively rich and flexible framework in which the frame and ramification problems can be solved in a systematic way by reasoning about default persistence of facts. (shrink)

"An important contribution to contemporary jurisprudential debate and to legal thought more generally, Just Interpretations is far ahead of currently available work."--Peter Goodrich, author of Oedipus Lex "I was struck repeatedly by the clarity of expression throughout the book. Rosenfeld's description and criticism of the recent work of leading thinkers distinguishes his work within the legal theory genre. Furthermore, his own theory is quite original and provocative."--Aviam Soifer, author of Law and the Company We Keep.

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.

One theoretical charge (of Optimality Theory in its early conception) must have been to retain that sense of qualitative particularity as affecting as constraining theory relevant to a proscribed field when clearly a motivation was to divine in circumscriptions operational consequences conceived on a deferred abstractive level. An attraction of the theory's embodying results of constraint interactions as responsive to theory-internal qualitative implementation, as being in fact supplementarily transparent to co-ordinations of variously language specific implementations, qualitative identifications, was apparent naturalistic (...) coordination of defined features taken here—in OT—at one fell-swoop. Differently put, the uses of analyses of the relevant types of spaces (‘primitive from the viewpoint of linguistic theories’) will (latterly) involve a period of time-stretch or compression over a previously normal (I take it) process of embeddings in a new theorised and recursively enacted invocation/re-invocation of base as digestively present in results of corrected theories. Or as Prince and Smolensky have it -/- 'What we have done, in essence, is to replace the iterative procedure (act/evaluate, act/evaluate, . . . ) with a recursive scheme: collect the results of all possible actions, then sort recursively.' OT, 16. (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)

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)

Biological taxonomists rely on the so-called ‘type method’ to regulate taxonomic nomenclature. For each newfound taxon, they lay down a ‘type specimen’ that carries with it the name of the taxon it belongs to. Even if a taxon’s circumscription is unknown and/or subject to change, it remains a necessary truth that the taxon’s type specimen falls within its boundaries. Philosophers have noted some time ago that this naming practice is in line with the causal theory of reference and its central (...) notion of rigid designation: a type specimen fixes the reference of a taxon name without defining it. Recently, however, this consensus has come under pressure in the pages of this journal. In a series of articles by Alex Levine, Joseph LaPorte, and Matthew Haber, it has been argued that type specimens belong only contingently to their species, and that this may bode problems for the relation between type method and causal theory. I will argue that this ‘contingency debate’ is a debate gone wrong, and that none of the arguments in defense of contingency withstand scrutiny. Taxonomic naming is not out of step with the causal theory, but conforms to it. However, I will also argue that this observation is itself in need of further explanation, since application of the type method in taxonomic practice is plagued by errors and ambiguities that threaten it with breaking down. Thus, the real question becomes why taxonomic naming conforms to the causal theory in the first place. I will show that the answer lies in the embedding of the type method into elaborate codes of nomenclature. (shrink)

Georg Henrik von Wright was not only the first interpreter of Wittgenstein, who argued that Spengler’s work had reinforced and helped Wittgenstein to articulate his view of life, but also the first to consider seriously that Wittgenstein’s attitude to his times makes him unique among the great philosophers, that the philosophical problems which Wittgenstein was struggling, indeed his view of the nature of philosophy, were somehow connected with features of our culture or civilization. -/- In this paper I draw inspiration (...) and courage from Von Wright’s insistence that trying to understand Wittgenstein in relation to his times is a philosophic task in its own right in order to probe into a relatively obscure region in Wittgenstein’s thought: his relation to the music of his times. It is a topic, on which Von Wright, and most other prominent Wittgenstein scholars, have said very little, but it is also one, which Wittgenstein himself attested was so important to him that he felt without it he was sure to be misunderstood. -/- I offer textual and historical evidence in support of my claim that, parallel to Wittgenstein’s exposure to Spengler’s Decline of the West in 1930, he was also introduced to the music theory of Heinrich Schenker, which helped him to articulate, partly by way of critique, a complex and unique position concerning the modern music of his times, which exhibits his rejection of what Von Wright later dubbed ‘the myth of progress’. As Von Wright observed in other regions of Wittgenstein’s work, he believed also with regards to the arts and to music in particular, neither in a brilliant future nor in the good old days. -/- I argue that Wittgenstein actually made a distinction between three kinds of modern music: (a) bad modern music, which is clearly a case of confusing means for ends, the hallmark of the myth of progress, as Von Wright observed; (b) vacuous modern music, which embodies some sort of diffidence, a difficulty to see through the omnipresence of what Von Wright called (following Habermas) a ‘colonialization’ of reified measures of progress; (c) good modern music, a paradoxical notion for Wittgenstein, which betokens the unlikely yet possible striving to penetrate through what appears as dissolution of the resemblances which unite this culture’s ways of life by rendering this condition as expressible and intransitively understandable. In the context of this third category, I offer an interpretation of Wittgenstein’s complex remarks on the music of Gustav Mahler, which palpably show that the problem of good modern music and the problem of philosophizing in the time of civilization were one and the same in Wittgenstein’s mind. -/- I conclude that, with regards to Von Wright’s own critical view of the modern myth of progress, we can learn from Wittgenstein that progress in the realm of art is closely aligned with the ideal of the perfection of man, yet transcending a social or political context. It is the ideal of cultural cohesion: affinity that the arts show to other human practices and cultural artifacts of its period. Wittgenstein’s tentative notion of good modern music (and its circumscription by his notion of the music of the future) may show its true colors when viewed in the context of Von Wright’s plea not to abandon work for progress as a critical task. (shrink)

The motivation of this study is that Reiter’s default theory as well as assumption-based argumentation frameworks corresponding to default theories have difficulties in handling disjunctive information, while a disjunctive default theory (ddt) avoids them. This paper presents the semantic correspondence between generalized assumption-based argumentation (ABA) and extended disjunctive logic programming as well as the correspondence between ABA and nonmonotonic reasoning approaches such as disjunctive default logic and prioritized circumscription. To overcome the above-mentioned difficulties of ABA frameworks corresponding to default (...) theories, we propose an assumption-based framework (ABF) translated from an extended disjunctive logic program (EDLP) since an EDLP can be translated into a ddt. Our ABF incorporates explicit negation and the connective of disjunction “|” to Heyninck and Arieli’s ABF induced by a disjunctive logic program. In this paper, first, we show how arguments are constructed from disjunctive rules in our proposed ABF. Then, we show the correspondence between answer sets of an EDLP P and stable extensions of the ABF translated from P with trivialization rules. After defining rationality postulates, we show answer sets of a consistent EDLP are captured by consistent stable extensions of the translated ABF with no trivialization rules. Finally, we show the correspondence between ABA and disjunctive default logic (resp. prioritized circumscription). The relation between ABA and possible model semantics of EDLPs is also discussed. (shrink)

The metaphysical possibility of agency at the phenomenal level, given the truth of a nomological and binding causal force, has long been a moot point in both Indian and western philosophical traditions. While an underlying implication of fatalistic resignation hangs over the possibility of phenomenal freedom within the ambit of the classical Indian interpretation of the Law of Karma, which forms the basis of the assumption that a fatalistic nexus of vāsanā (cravings for mundane achievements) and the ensuing karma (action-tendencies (...) to reach a mundane goal) circumscribes an agent’s choices, the western thought on the question of the freedom of choice has rather been preoccupied with the putative threat posed by the deterministic law of various nuances, such as theological determinism and logical determinism. A close analysis of the western philosophical debate surrounding free will reveals that the kind of linear causation that determinism supposedly entails is the primary reason for its being conflated with fatalism. The source of all the misgiving about determinism’s free will subduing influence is the oversight that it renders the agent’s rational endeavour a futile exercise in the same way as fatalism does. In this paper, therefore, an attempt has been made to disentangle determinism from fatalism. A key proposal advanced in this paper is that the causative force of the karmic law, admitted by most of the classical schools of Indian philosophy, may prima facie have a circumscriptive effect on agentic rational pursuits and choices. However, an intimate study reveals that this law does not preclude phenomenal freedom, although of a higher echelon. The classical Indian schools of philosophy admitting the undeniable presence of this karmic law allow the possibility of this seemingly inexorable causative force of the law being overridden by a more reason-guided pursuit, adopted by the agent, after an overhaul of his egoistic cravings. The model of agency developed in this paper is based on the claim that it is by way of undergoing self-determination that phenomenal freedom reaches its pinnacle. Drawing on the theories of volition and self advanced by some prominent classical Indian philosophical schools and the classical western philosophical theories of free will in the light of the deterministic threat, an attempt has been made to bring into harmony the rhetoric of both worlds, exploring the possibility whether phenomenal freedom can be salvaged through agentic self-determination and self-development. (shrink)

In this paper, I elaborate a Derridean deconstruction of law through the lens of Lacanian psychoanalysis. Derrida only focuses on jurisprudential law enforcement in his famous ‘Force of Law’ lecture, leaving corporeal law enforcement untouched. In turn, I explore the irresolvable conceptual tensions within corporeal law enforcement from the standpoints of (a) individuals rationalizing their obedience to law enforcement and (b) the legal system rationalizing its circumscription of acceptable law enforcement. To support my analysis, I examine landmark court cases and (...) their deleterious effects on accountability for law enforcers. In particular, I track the progression from the legal standard of ‘shock of conscience’ (i.e., established by Rochin v. California (1952)) to that of ‘objective reasonableness’ (i.e., established by Graham v. Connor (1989)), which reinforces the legal protections for and libidinal features of police brutality. In this sense, I seek to clarify the dimensions of the libidinal economy belonging to policy brutality, namely its components of sadism and superegoic enjoyment. (shrink)

We present an axiomatization of a problem in commonsense reasoning, characterizing the proper procedure for cracking an egg and transferring its contents to a bowl. The axiomatization is mid-sized, larger than toy problems such as the Yale Shooting Problem or the Suitcase Problem, but much smaller than the comprehensive axiomatizations associated with CYC and HPKB. This size of axiomatization permits the development of non-trivial, reusable core theories of commonsense reasoning, acts as a testbed for existing theories of commonsense (...) reasoning, and encourages the discovery of new problems in commonsense reasoning.We present portions of core theories of containment, falling, and pouring, integrated into Shanahan's circumscriptive event calculus, and show how these can serve as the basis of an axiomatization that partly characterizes egg cracking. We discuss several commonsense reasoning problems encountered during this research, such as the Initial Specification Problem (a relative of the frame problem that occurs in theories in which fluents can trigger actions), and the Unobtainable State Problem (the problem of determining whether or not a theorem stating that one cannot get from one state to another is meaningful). (shrink)

This article is concerned with the question of the proper place of substantial general metaphysics in aesthetics and the philosophy of art. For reasons articulated in writings from the 1950s, analytic aesthetics denies that there is any relation of dependence and regards the intrusion of metaphysics into reflection on art as not merely superfluous but also methodologically inappropriate. Against this I argue that analytic aesthetics in its circumscription of the bounds of the discipline is not metaphysically neutral, that it is (...) vulnerable to the challenge of scientific naturalism, and that a case for the necessity of metaphysics in aesthetics and the philosophy of art can be made on the grounds of the constitutive opacity of art and the aesthetic from the standpoint of ordinary consciousness. The analytic reception of Kant’s aesthetic theory, I argue, supports this conclusion. (shrink)

Lifschitz introduced the notion of defining extensions of predicate default theories not as absolute, but relative to a specified domain. We look specifically at default theories over a countable domain and show the set of default theories which possess an ω -extension is Σ 2 1 -complete. That the set is in Σ 2 1 is shown by writing a nearly circumscriptive formula whose ω -models correspond to the ω -extensions of a given default theory; similarly, (...) Σ 2 1 -hardness is established by a method for translating formulas into default theories in such a way that ω -models of the circumscriptive formula correspond to ω -extensions of the default theory. (shrink)

This thesis analyzes from a philosophical perspective different models for nonmonotonic inference, belief revision and the handling of inconsistencies. ;The first chapter serves as an introduction to the subject, giving examples and analyzing the main concepts. As a result of these discussions, this thesis tries to: produce a refined map of the main notions related to this subject, maintain that there can be a fault tolerant logic that stands in support of fault tolerant reasoning, and defend the use of deductive (...) databases as models for changes of belief. ;The second chapter explores monotonic proposals to deal with uncertain reasoning. These include logics based on a classical notion of consequence, interpretations of defeasible reasoning as containing implicit premises, and systems in which temporal change is an integral part of the representation of states of affairs, via temporal indices or more elaborate devices. ;The third chapter explores quantitative approaches to nonmonotonic reasoning like dispositional logic, and theories of probabilistic reasoning including Bayesian, certainty factors, and Dempster-Shafer. ;The fourth chapter explores qualitative approaches. Here we mention conditional, default, and nonmonotonic logics, and the circumscription and autoepistemic formalisms. ;The fifth chapter studies different proposals to deal with contradictions. It starts with a review of the types of belief inconsistencies, and then it presents mechanisms to prevent, control or correct them. I explore paraconsistent logics, specially relevance logics, to "bracket" the area of conflict and allow inferences about non-related topics to continue unaffected. Then I examine different methods to get rid of the inconsistencies, including the use of dependency-directed backtracking and of relevance logic. ;Finally, I present my conclusions, and mention some of the open problems. (shrink)

I analyze the frame problem and its relation to other epistemological problems for artificial intelligence, such as the problem of induction, the qualification problem and the "general" AI problem. I dispute the claim that extensions to logic (default logic and circumscriptive logic) will ever offer a viable way out of the problem. In the discussion it will become clear that the original frame problem is really a fairy tale: as originally presented, and as tools for its solution are circumscribed (...) by Pat Hayes, the problem is entertaining, but incapable of resolution. The solution to the frame problem becomes available, and even apparent, when we remove artificial restrictions on its treatment and understand the interrelation between the frame problem and the many other problems for artificial epistemology. I present the solution to the frame problem: an adequate theory and method for the machine induction of causal structure. Whereas this solution is clearly satisfactory in principle, and in practice real progress has been made in recent years in its application, its ultimate implementation is in prospect only for future generations of AI researchers. (shrink)

When I was invited by Yale University to deliver the Cassirer lectures, I hesitated for a topic. I wanted something new. I proposed the emotions, and at that time my knowledge of the topic was so slight that I didn't know whether it was something that I had already written on or not.I mention this fact because one thing that I have since learnt about the emotions is that such ignorance is in order. For it is one of those topics (...) where grasping the extension of the term is inseparable from having some theory of the matter, however primitive. One way to explain this fact is to invoke the novelty of the term, for, in the sense in which it is used in this lecture, it is only about 300 years old. Another way, probably related, is to point to the fact that, not only are there belief and particular beliefs, desire and particular desires, but, when we refer to particular beliefs and to particular desires, we call them ‘the belief that this’ or ‘the desire that that’. However there is no locution ‘the emotion that this’, or ‘the emotion that that’, which would indicate the presence of an emotion. It seems that ordinary language is an intermittent guide to the circumscription of the emotions. (shrink)

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)