Combinator Logics

Combinator logics are a broad family of substructual logics that are formed by extending the basic relevant logic B with axioms that correspond closely to the reduction rules of proper combinators in combinatory logic. In the Routley-Meyer relational semantics for relevant logic each such combinator logic is characterized by the class of frames that meet a first-order condition that also directly corresponds to the same combinator's reduction rule. A second family of logics is also introduced that extends B with the addition of propositional constants that correspond to combinators. These are characterized by relational frames that meet first-order conditions that reflect the structures of the combinators themselves.     

Reasoning through doing. Epistemic mediators in scientific discovery

The recent epistemological and cognitive studies concentrate on the concept of abduction, as a means to originate and refine new ideas. Traditional cognitive science and computational accounts concerning abduction aim at illustration discovery and creativity processes in terms of theoretical and “internal” aspects, by means of computational simulations and/or abstract cognitive models. I will illustrate in this paper that some typical internal abductive processes are involved in scientific reasoning and discovery (for example through radical innovations). Nevertheless, especially concrete manipulations of the external world constitute a fundamental passage in science: by a process of manipulative abduction it is possible to build prostheses (epistemic mediators) for human minds, by interacting with external objects and representations in a constructive way. In this manner it is possible to create implicit knowledge through doing and to produce various opportunity to find, for example, anomalies and fruitful new risky perspectives. This kind of embodied and unexpressed knowledge holds a key role in the subsequent processes of scientific comprehension and discovery.     

Epistemology and artificial intelligence

In this essay we advance the view that analytical epistemology and artificial intelligence are complementary disciplines. Both fields study epistemic relations, but whereas artificial intelligence approaches this subject from the perspective of understanding formal and computational properties of frameworks purporting to model some epistemic relation or other, traditional epistemology approaches the subject from the perspective of understanding the properties of epistemic relations in terms of their conceptual properties. We argue that these two practices should not be conducted in isolation. We illustrate this point by discussing how to represent a class of inference forms found in standard inferential statistics. This class of inference forms is interesting because its members share two properties that are common to epistemic relations, namely defeasibility and paraconsistency. Our modeling of standard inferential statistical arguments exploits results from both logical artificial intelligence and analytical epistemology. We remark how our approach to this modeling problem may be generalized to an interdisciplinary approach to the study of epistemic relations.     

An analytic tableau calculus for a temporalised belief logic

A tableau is a refutation-based decision procedure for a related logic, and is among the most popular proof procedures for modal logics. In this paper, we present a labelled tableau calculus for a temporalised belief logic called TML⁺, which is obtained by adding a linear-time temporal logic onto a belief logic by the temporalisation method of Finger and Gabbay. We first establish the soundness and the completeness of the labelled tableau calculus based on the soundness and completeness results of its constituent logics. We then sketch a resolution-type proof procedure that complements the tableau calculus and also propose a model checking algorithm for TML⁺ based on the recent results for model checking procedures for temporalised logics. TML⁺ is suitable for formalising trust and agent beliefs and reasoning about their evolution for agent-based systems. Based on the logic TML⁺, the proposed labelled tableau calculus could be used for analysis, design and verification of agent-based systems operating in dynamic environments.     

Applied Logic without Psychologism

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance.     

Majority merging by adaptive counting

The present paper introduces a belief merging procedure by majority using the standard format of Adaptive Logics. The core structure of the logic ADM ^c (Adaptive Doxastic Merging by Counting) consists in the formulation of the conflicts arising from the belief bases of the agents involved in the procedure. A strategy is then defined both semantically and proof-theoretically which selects the consistent contents answering to a majority principle. The results obtained are proven to be equivalent to a standard majority operator for bases with partial support.     

The virtues of epistemic conservatism

Although several important methodologies implicitly assume the truth of epistemic conservatism, the view that holding a belief confers some measure of justification on the belief, recent criticisms have led some to conclude that epistemic conservatism is an implausible view. That conclusion is mistaken. In this article, I propose a new formulation of epistemic conservatism that is not susceptible to the criticisms leveled at earlier formulations of epistemic conservatism. In addition to withstanding these criticisms, this formulation of epistemic conservatism has several benefits. First, this formulation has the benefits of earlier formulations of epistemic conservatism, that is to say it makes sense of our intuitions about justification in regard to both memory beliefs and beliefs for which we have forgotten our evidence. Second, it provides a good way of responding to the skeptic’s challenge concerning the possibility of possessing knowledge of the external world posed by the Alternative Hypotheses argument. Third, it provides responses to both forms of a new skeptical problem plaguing basic knowledge structure theories, the Problem of Easy Knowledge formulated by Stewart Cohen. I argue that given the many benefits of this formulation of epistemic conservatism and the fact that it is not vulnerable to the criticisms that undermine earlier formulations of epistemic conservatism, this formulation of epistemic conservatism is a plausible view to maintain.     

The Basic Constructive Logic for a Weak Sense of Consistency defined with a Propositional Falsity Constant

The logic B_Kc1 is the basic constructive logic in the ternaryrelational semantics (without a set of designated points) adequateto consistency understood as the absence of the negation ofany theorem. Negation is introduced in B_Kc1 with a negationconnective. The aim of this paper is to define the logic B_Kc1F.In this logic negation is introduced via a propositional falsityconstant. We prove that B_Kc1 and B_Kc1F are definitionally equivalent.     

The indexicality of ‘knowledge’

Epistemic contextualism—the view that the content of the predicate ‘know’ can change with the context of utterance—has fallen into considerable disrepute recently. Many theorists have raised doubts as to whether ‘know’ is context-sensitive, typically basing their arguments on data suggesting that ‘know’ behaves semantically and syntactically in a way quite different from recognised indexicals such as ‘I’ and ‘here’ or ‘flat’ and ‘empty’. This paper takes a closer look at three pertinent objections of this kind, viz. at what I call the Error-Theory Objection, the Gradability Objection and the Clarification-Technique Objection. The paper concludes that none of these objections can provide decisive evidence against contextualism.     

Quantification over Sets of Possible Worlds in Branching-Time Semantics

Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quantification over histories, which is a second-order quantification over sets of possible worlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as first-order counterparts of the original semantics.