Applications of Intuitionistic Logic in Answer Set Programming

We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence notions and their applications are discussed. Some results on intermediate logics are shown, and applied later to prove properties of answer sets. A characterization of answer sets for logic programs with nested expressions is provided in terms of intuitionistic provability, generalizing a recent result given by Pearce. It is known that the answer set semantics for logic programs with nested expressions may select non-minimal models. Minimal models can be very important in some applications, therefore we studied them; in particular we obtain a characterization, in terms of intuitionistic logic, of answer sets which are also minimal models. We show that the logic G3 characterizes the notion of strong equivalence between programs under the semantic induced by these models. Finally we discuss possible applications and consequences of our results. They clearly state interesting links between ASP and intermediate logics, which might bring research in these two areas together.Comment: 30 pages, Under consideration for publication in Theory and Practice of Logic Programmin

Epistemic Luck

Epistemic luck is a generic notion used to describe any of a number of ways in which it can be accidental, coincidental, or fortuitous that a person has a true belief. For example, one can form a true belief as a result of a lucky guess, as when one believes through guesswork that “C” is the right answer to a multiple-choice question and one’s belief just happens to be correct. One can form a true belief via wishful thinking; for example, an optimist’s belief that it will not rain may luckily turn out to be correct, despite forecasts for heavy rain all day. One can reason from false premises to a belief that coincidentally happens to be true. One can accidentally arrive at a true belief through invalid or fallacious reasoning. And one can fortuitously arrive at a true belief from testimony that was intended to mislead but unwittingly reported the truth. In all of these cases, it is just a matter of luck that the person has a true belief. Until the twenty-first century, there was nearly universal agreement among epistemologists that epistemic luck is incompatible with knowledge. Call this view “the incompatibility thesis.” In light of the incompatibility thesis, epistemic luck presents epistemologists with three distinct but related challenges. The first is that of providing an accurate analysis of knowledge (in terms of individually necessary and jointly sufficient conditions for “S knows that p,” where ‘S’ represents the knower and ‘p’ represents the proposition known). An adequate analysis of knowledge must succeed in specifying conditions that rule out all instances of knowledge-destroying epistemic luck. The second challenge is to resolve the skeptical paradox that the ubiquity of epistemic luck generates: As will become clear in section 2c, epistemic luck is an all-pervasive phenomenon. Coupling this fact with the incompatibility thesis entails that we have no propositional knowledge. The non-skeptical epistemologist must somehow reconcile the strong intuition that epistemic luck is not compatible with knowledge with the equally evident observation that it must be. The third challenge concerns the special skeptical threat that epistemic luck seems to pose for more reflective forms of knowledge, such as knowing that one knows. Each of these challenges will be explored in the present article

Skepticism Motivated: On the Skeptical Import of Motivated Reasoning

Empirical work on motivated reasoning suggests that our judgments are influenced to a surprising extent by our wants, desires and preferences (Kahan 2016; Lord, Ross, and Lepper 1979; Molden and Higgins 2012; Taber and Lodge 2006). How should we evaluate the epistemic status of beliefs formed through motivated reasoning? For example, are such beliefs epistemically justified? Are they candidates for knowledge? In liberal democracies, these questions are increasingly controversial as well as politically timely (Beebe et al. 2018; Lynch forthcoming, 2018; Slothuus and de Vreese 2010). And yet, the epistemological significance of motivated reasoning has been almost entirely ignored by those working in mainstream epistemology. We aim to rectify this oversight. Using politically motivated reasoning as a case study, we show how motivated reasoning gives rise to three distinct kinds of skeptical challenges. We conclude by showing how the skeptical import of motivated reasoning has some important ramifications for how we should think about the demands of intellectual humility

Fear expression and return of fear following threat instruction with or without direct contingency experience

Prior research showed that mere instructions about the contingency between a conditioned stimulus (CS) and an unconditioned stimulus (US) can generate fear reactions to the CS. Little is known, however, about the extent to which actual CS US contingency experience adds anything beyond the effect of contingency instructions. Our results extend previous studies on this topic in that it included fear potentiated startle as an additional dependent variable and examined return of fear (ROF) following reinstatement. We observed that CS US pairings can enhance fear reactions beyond the effect of contingency instructions. Moreover, for all measures of fear, instructions elicited immediate fear reactions that could not be completely overridden by subsequent situational safety information. Finally, ROF following reinstatement for instructed CS+s was unaffected by actual experience. In summary, our results demonstrate the power of contingency instructions and reveal the additional impact of actual experience of CS US pairings

Artificial Brains and Hybrid Minds

The paper develops two related thought experiments exploring variations on an ‘animat’ theme. Animats are hybrid devices with both artificial and biological components. Traditionally, ‘components’ have been construed in concrete terms, as physical parts or constituent material structures. Many fascinating issues arise within this context of hybrid physical organization. However, within the context of functional/computational theories of mentality, demarcations based purely on material structure are unduly narrow. It is abstract functional structure which does the key work in characterizing the respective ‘components’ of thinking systems, while the ‘stuff’ of material implementation is of secondary importance. Thus the paper extends the received animat paradigm, and investigates some intriguing consequences of expanding the conception of bio-machine hybrids to include abstract functional and semantic structure. In particular, the thought experiments consider cases of mind-machine merger where there is no physical Brain-Machine Interface: indeed, the material human body and brain have been removed from the picture altogether. The first experiment illustrates some intrinsic theoretical difficulties in attempting to replicate the human mind in an alternative material medium, while the second reveals some deep conceptual problems in attempting to create a form of truly Artificial General Intelligence

Safety, the Preface Paradox and Possible Worlds Semantics

This paper contains an argument to the effect that possible worlds semantics renders semantic knowledge impossible, no matter what ontological interpretation is given to possible worlds. The essential contention made is that possible worlds semantic knowledge is unsafe and this is shown by a parallel with the preface paradox