I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

It is argued that given the “anti-anthropomorphic” principle—that the universe is not structured for our benefit—modelling trade-offs will necessarily mean that many of our models will be context-specific. It is argued that context-specificity is not the same as relativism. The “context heuristic”—that of dividing processing into rich, fuzzy context-recognition and crisp, conscious reasoning and learning—is outlined. The consequences of accepting the impact of this human heuristic in the light of the necessity of accepting context-specificity in our modelling of complex systems (...) is examined. In particular the development of “islands” or related model clusters rather than over-arching laws and theories. It is suggested that by accepting and dealing with context (rather than ignoring it) we can push the boundaries of science a little further. (shrink)

http://www.cs.bham.ac.uk/research/projects/cogaff/62-80.html#1967-01.

As many philosophers agree, the frame problem is concerned with how an agent may efficiently filter out irrelevant information in the process of problem-solving. Hence, how to solve this problem hinges on how to properly handle semantic relevance in cognitive modeling, which is an area of cognitive science that deals with simulating human's cognitive processes in a computerized model. By "semantic relevance", we mean certain inferential relations among acquired beliefs which may facilitate information retrieval and practical reasoning under certain epistemic (...) constraints, e. g., the insufficiency of knowledge, the limitation of time budget, etc. However, traditional approaches to relevance—as for example, relevance logic, the Bayesian approach, as well as Description Logic—have failed to do justice to the foregoing constraints, and in this sense, they are not proper tools for solving the frame problem/relevance problem. As we will argue in this paper, Non-Axiomatic Reasoning System (NARS) can handle the frame problem in a more proper manner, because the resulting solution seriously takes epistemic constraints on cognition as a fundamental theoretical principle. (shrink)

Situations serving as partial worlds as well as events in natural language semantics are constructed from a type-theoretic interpretation of firstorder formulae and (after a type reduction) temporal formulae. Limitations of the Russell-Wiener-Kamp derivation of time from events are discussed and overcome to give a more widely applicable account of temporal granularity. Finite situations are formulated as strings of observations, conceptualized to persist inertially (in the absence of forces).

Relations computed by finite-state transducers are applied to interpret temporal propositions in terms of strings representing finite contexts or situations. Carnap–Montague intensions mapping indices to extensions are reformulated as relations between strings that can serve as indices and extensions alike. Strings are related according to information content, temporal span and granularity, the bounds on which reflect the partiality of natural language statements. That partiality shapes not only strings-as-extensions (indicating what statements are about) but also strings-as-indices (underlying truth conditions).

The frame problem is a problem in artificial intelligence that a number of philosophers have claimed has philosophical relevance. The structure of this paper is as follows: (1) An account of the frame problem is given; (2) The frame problem is distinguished from related problems; (3) The main strategies for dealing with the frame problem are outlined; (4) A difference between commonsense reasoning and prediction using a scientific theory is argued for; (5) Some implications for the..

This chapter investigates the computational consequences of a broadly Gricean view of language use as intentional activity. In this view, dialogue rests on coordinated reasoning about communicative intentions. The speaker produces each utterance by formulating a suitable communicative intention. The hearer understands it by recognizing the communicative intention behind it. When this coordination is successful, interlocutors succeed in considering the same intentions— that is, the same representations of utterance meaning—as the dialogue proceeds. In this paper, I emphasize that these intentions (...) can be formalized; we can provide abstract but systematic representations that spell out what a speaker is trying to do with an utterance. Such representations describe utterances simultaneously as the product of our knowledge of grammar and as actions chosen for a reason. In particular, they must characterize the speaker’s utterance in grammatical terms, provide the links to the context that the grammar requires, and so arrive at a contribution that the speaker aims to achieve. Because I have implemented this formalism, we can regard it as a possible analysis of conversational processes at the level of computational theory. Nevertheless, this analysis leaves open what the nature of the biological computation involved in inference to intentions is, and what regularities in language use support this computation. (shrink)

By what empirical means can a person determine whether he or she is presently awake or dreaming? Any conceivable test addressing this question, which is a special case of the classical metaphysical doubting of reality, must be statistical (for the same reason that empirical science is, as noted by Hume). Subjecting the experienced reality to any kind of statistical test (for instance, a test for bizarreness) requires, however, that a set of baseline measurements be available. In a dream, or in (...) a simulation, any such baseline data would be vulnerable to tampering by the same processes that give rise to the experienced reality, making the outcome of a reality test impossible to trust. Moreover, standard cryptographic defenses against such tampering cannot be relied upon, because of the potentially unlimited reach of reality modification within a dream, which may range from the integrity of the verification keys to the declared outcome of the entire process. In the face of this double predicament, the rational course of action is to take reality at face value. The predicament also has some intriguing corollaries. In particular, even the most revealing insight that a person may gain into the ultimate nature of reality (for instance, by attaining enlightenment in the Buddhist sense) is ultimately unreliable, for the reasons just mentioned. At the same time, to adhere to this principle, one has to be aware of it, which may not be possible in various states of reduced or altered cognitive function such as dreaming or religious experience. Thus, a subjectively enlightened person may still lack the one truly important piece of the puzzle concerning his or her existence. (shrink)

cuted actions. It has been applied to several challenge problems in the theory of commonsense knowledge. We study the relationship between this formalism and other work on nonmonotonic reasoning and knowl-.

Events employed in natural language semantics are characterized in terms of regular languages, each string in which can be regarded as a motion picture. The relevant finite automata then amount to movie cameras/projectors, or more formally, to finite Kripke structures with par- tial valuations. The usual regular constructs (concatena- tion, choice, etc) are supplemented with superposition of strings/automata/languages, realized model-theoretically as conjunction.

We present an approach to combining three areas of research which we claim are all based on information theory: knowledge representation in Artificial Intelligence and Cognitive Science using prototypes, plans, or schemata; formal semantics in natural language, especially the semantics of the `if-then' conditional construct; and the logic of subjunctive conditionals first developed using a possible worlds semantics by Stalnaker and Lewis. The basic premise of the paper is that both schema-based inference and the semantics of conditionals are based on (...) Dretske's notion of information flow and Barwise and Perry's notion of a constraint in situation semantics. That is, the connection between antecedent and consequent of a conditional `if were the case then would be the case' is an informational relation holding with respect to a pragmatically determined utterance situation. The bridge between AI and conditional logic is that a prototype or planning schema represents a situation type, and the background assumptions underlying the application of a schema in a situation correspond to channel conditions on the flow of information. Adapting the work of Stalnaker and Lewis, the semantics of conditionals is modeled by a refinement ordering on situations: a conditional `if then ' holds with respect to a situation if all the minimal refinements of the situation that support also support . We present new logics of situations, information flow, and subjunctive conditionals based on three-valued partial logic that formalizes our approach, and conclude with a discussion of the resulting theory of conditionals, including the "paradoxes" of conditional implication, the difference between truth conditions and assertability conditions for subjunctive conditionals, and the relationship between subjunctive and indicative conditionals. (shrink)

Temporal propositions are mapped to sets of strings that witness (in a precise sense) the propositions over discrete linear Kripke frames. The strings are collected into regular languages to ensure the decidability of entailments given by inclusions between languages. (Various notions of bounded entailment are shown to be expressible as language inclusions.) The languages unwind computations implicit in the logical (and temporal) connectives via a system of finite-state constraints adapted from finite-state morphology. Applications to Hybrid Logic and non-monotonic inertial reasoning (...) are briefly considered. (shrink)

Severity of Test (SoT) is an alternative to Popper's logical falsification that solves a number of problems of the logical view. It was presented by Popper himself in 1963. SoT is a less sophisticated probabilistic model of hypothesis testing than Oaksford & Chater's (O&C's) information gain model, but it has a number of striking similarities. Moreover, it captures the intuition of everyday hypothesis testing.

Human cognition requires coping with a complex and uncertain world. This suggests that dealing with uncertainty may be the central challenge for human reasoning. In Bayesian Rationality we argue that probability theory, the calculus of uncertainty, is the right framework in which to understand everyday reasoning. We also argue that probability theory explains behavior, even on experimental tasks that have been designed to probe people's logical reasoning abilities. Most commentators agree on the centrality of uncertainty; some suggest that there is (...) a residual role for logic in understanding reasoning; and others put forward alternative formalisms for uncertain reasoning, or raise specific technical, methodological, or empirical challenges. In responding to these points, we aim to clarify the scope and limits of probability and logic in cognitive science; explore the meaning of the explanation of cognition; and re-evaluate the empirical case for Bayesian rationality. (shrink)

We describe how Intuitionistic Linear Logic can be used to provide a unified logical account for agents to find and execute plans. This account supports the modelling of agent interaction, including dialogue; allows agents to be robust to unexpected events and failures; and supports significant reuse of agent specifications. The framework has been implemented and several case studies have been considered. Further applications include human–computer interfaces as well as agent interaction in the semantic web.

Here I consider the relative merits of two recent models of explanation, James Woodward's interventionist-counterfactual model and the model model. According to the former, explanations are largely constituted by information about the consequences of counterfactual interventions. Problems arise for this approach because countless relevant interventions are possible in most cases and because it overlooks other kinds of equally relevant information. According the model model, explanations are largely constituted by cognitive models of actual mechanisms. On this approach, explanations tend not to (...) represent any of the aforementioned information explicitly but can instead be used to produce it on demand. The model model thus offers the more plausible account of the information of which we are aware when we have an explanation and of the ratiocinative process through which we derive many kinds of information that are relevant to the evaluation of explanations. (shrink)

A plan is made to fly from Glasgow to Moscow and is shown by circumscription to lead to the traveller arriving in Moscow. Then a fact about an unexpected obstacle---the traveller losing his ticket---is added without changing any of the previous facts, and the original plan can no longer be shown to work if it must take into account the new fact. However, an altered plan that includes buying a replacement ticket can now be shown to work. The formalism used (...) is a modification of one developed by Vladimir Lifschitz, and I have been informed that the modification isn't correct, and I should go back to Lifschitz's original formalism. April 14,2001: I still haven't done it, so this article has to be regarded as tentative. I hope to fix the problems without going back to Lifschitz's formalism, which I find awkward.}. (shrink)

“Everyone knows that language is variable.” This is the bald sentence with which Sapir (1921:147) begins his chapter on language as an historical product. He goes on to emphasize how two speakers’ usage is bound to differ “in choice of words, in sentence structure, in the relative frequency with which particular forms or combinations of words are used”. I should add that much sociolinguistic and historical linguistic research has shown that the same speaker’s usage is also variable (Labov 1966, Kroch (...) 2001:722). However, the tradition of most syntacticians has been to ignore this thing that everyone knows. (shrink)

Reichenbach's event, reference and speech times are interpreted semantically by stringing and superposing sets of temporal formulae, structured within regular languages. Notions of continuation branches and of inertia, bound (in a precise sense) by reference time, are developed and applied to the progressive and the perfect.

In artificial intelligence (AI), a number of criticisms were raised against the use of probability for dealing with uncertainty. All these criticisms, except what in this article we call the non-adequacy claim, have been eventually confuted. The non-adequacy claim is an exception because, unlike the other criticisms, it is exquisitely philosophical and, possibly for this reason, it was not discussed in the technical literature. A lack of clarity and understanding of this claim had a major impact on AI. Indeed, mostly (...) leaning on this claim, some scientists developed an alternative research direction and, as a result, the AI community split in two schools: a probabilistic and an alternative one. In this article, we argue that the non-adequacy claim has a strongly metaphysical character and, as such, should not be accepted as a conclusive argument against the adequacy of probability. (shrink)

Events and situations are represented by strings of temporally ordered observations, on the basis of which the events and situations are recognized. Allen’s basic interval relations are derived from superposing strings that mark interval boundaries, and Kamp’s event structures are constructed as projective limits of strings. Observations are generalized to temporal propositions, leading to event-types that classify event-instances. Working with sets of strings built from temporal propositions, we obtain natural notions of bounded entailment from set inclusions. These inclusions are decidable (...) if the sets are accepted by finite automata. (shrink)

Anankastic conditionals are analyzed in terms of events conceived as sequences of snapshots – roughly, comics. Quantification is applied not to worlds (sets of which are customarily identified with propositions) but to strings that record observations of actions. The account generalizes to other types of conditionals, sidestepping certain well-known problems that beset possible worlds treatments, such as logical omniscience and irrelevance. A refinement for anankastic conditionals is considered, incorporating action relations.

A fundamental question in reasoning about change is, what information does a reasoning agent infer about later times from earlier times? I will argue that reasoning about change by an agent is to be modeled in terms of the persistence of the agent''s beliefs over time rather than the persistence of truth and that such persistence is explained by pragmatic factors about how agents acquire information from other agents rather than by general principles of persistence about states of the world. (...) AI accounts of persistence have focused on closed world examples of change, in which the agent believes that the truth of a proposition is unaltered so long as he or she has no evidence that it has been changed. AI principles of persistence seem plausible in a closed world where one assumes the agent knows everything that is happening. If one drops the assumption of omniscience, however, the analysis of persistence is implausible. To get a good account of persistence and reasoning about change, I argue we should examine open world examples of change, in which the agent is ignorant of some of the changes occurring in the world. In open world examples of change, persistence must be formulated, I argue, as a pragmatic principle about the persistence of beliefs. After elaborating my criticisms of current accounts of persistence, I examine how such pragmatic principles fare with the notorious examples of reasoning about action that have collectively characterized the so-called frame problem. (shrink)

This paper argues that chance (risk or opportunity) discovery is challenging, from a reasoning point of view, because it represents a dilemma for inductive reasoning. Chance discovery shares many features with the grue paradox. Consequently, Bayesian approaches represent a potential solution. The Bayesian solution evaluates alternative models generated using a temporal logic planner to manage the chance. Surprise indices are used in monitoring the conformity of the real world and the assessed probabilities. Game theoretic approaches are proposed to deal with (...) multi-agent interaction in chance management. (shrink)

The idea that natural language grammar and planned action are relatedsystems has been implicit in psychological theory for more than acentury. However, formal theories in the two domains have tendedto look very different. This article argues that both faculties sharethe formal character of applicative systems based on operationscorresponding to the same two combinatory operations, namely functional composition and type-raising. Viewing them in thisway suggests simpler and more cognitively plausible accounts of bothsystems, and suggests that the language faculty evolved in the (...) speciesand develops in children by a rather direct adaptation of a moreprimitive apparatus for planning purposive action in the world bycomposing affordances of objects or tools. Theknowledge representation that underlies such planning is alsoreflected in the natural language semantics of tense, mood, andaspect, which the paper begins by arguing provides the key tounderstanding both systems. (shrink)

This paper presents an approach to artificial intelligence planning based on linear temporal logic (LTL). A simple and easy-to-use planning language is described, Planning Domain Description Language with control Knowledge (PDDL-K), which allows one to specify a planning problem together with heuristic information that can be of help for both pruning the search space and finding better quality plans. The semantics of the language is given in terms of a translation into a set of LTL formulae. Planning is then reduced (...) to “executing” the LTL encoding, i.e. to model search in LTL. The feasibility of the approach has been successfully tested by means of the system Pdk, an implementation of the proposed method. (shrink)

Most agents can acquire information about their environments as they operate. A good plan for such an agent is one that not only achieves the goal, but is also executable, i.e., ensures that the agent has enough information at every step to know what to do next. In this paper, we present a formal account of what it means for an agent to know how to execute a plan and to be able to achieve a goal. Such a theory is (...) a prerequisite for producing specifications of planners for agents that can acquire information at run time. It is also essential to account for cooperation among agents. Our account is more general than previous proposals, correctly handles programs containing loops, and incorporates a solution to the frame problem. It can also be used to prove programs containing sensing actions correct. (shrink)

While we agree that the frame problem, as initially stated by McCarthy and Hayes (1969), is a problem that arises because of the use of representations, we do not accept the anti-representationalist position that the way around the problem is to eliminate representations. We believe that internal representations of the external world are a necessary, perhaps even a defining feature, of higher cognition. We explore the notion of dynamically created context-dependent representations that emerge from a continual interaction between working memory, (...) external input, and long-term memory. We claim that only this kind of representation, necessary for higher cognitive abilities such as counterfactualization, will allow the combinatorial explosion inherent in the frame problem to be avoided. (shrink)

A situated agent is one which operates within an environment. In most cases, the environment in which the agent exists will be more complex than the agent itself. This means that an agent, human or artificial, which wishes to carry out non-trivial operations in its environment must use techniques which allow an unbounded world to be represented within a cognitively bounded agent. We present a brief description of some important theories within the fields of epistemology and metaphysics. We then discuss (...) ways in which philosophical problems of scepticism are related to the problems faced by knowledge representation. We suggest that some of the methods that philosophers have developed to address the problems of epistemology may be relevant to the problems of representing knowledge within artificial agents. (shrink)

These notes discuss self-awareness in humans and machines. The goal is to determine useful forms of machine self-awareness and also those that are on the road to human-level AI. This is a draft which is to be improved, and suggestions are solicited. There are a few formulas in this version. The final version will have more.