Lower complexity bounds in justification logic

Justification Logic studies epistemic and provability phenomena by introducing justifications/proofs into the language in the form of justification terms. Pure justification logics serve as counterparts of traditional modal epistemic logics, and hybrid logics combine epistemic modalities with justification terms. The computational complexity of pure justification logics is typically lower than that of the corresponding modal logics. Moreover, the so-called reflected fragments, which still contain complete information about the respective justification logics, are known to be in~NP for a wide range of justification logics, pure and hybrid alike. This paper shows that, under reasonable additional restrictions, these reflected fragments are NP-complete, thereby proving a matching lower bound. The proof method is then extended to provide a uniform proof that the corresponding full pure justification logics are $\Pi^p_2$-hard, reproving and generalizing an earlier result by Milnikel.

How can computer simulations produce new knowledge?

It is often claimed that scientists can obtain new knowledge about nature by running computer simulations. How is this possible? I answer this question by arguing that computer simulations are arguments. This view parallels Norton’s argument view about thought experiments. I show that computer simulations can be reconstructed as arguments that fully capture the epistemic power of the simulations. Assuming the extended mind hypothesis, I furthermore argue that running the computer simulation is to execute the reconstructing argument. I discuss some objections and reject the view that computer simulations produce knowledge because they are experiments. I conclude by comparing thought experiments and computer simulations, assuming that both are arguments.

Why Monte Carlo Simulations are Inferences and not Experiments

Monte Carlo simulations arrive at their results by introducing randomness, sometimes derived from a physical randomizing device. Nonetheless, we argue, they open no new epistemic channels beyond that already employed by traditional simulations: the inference by ordinary argumentation of conclusions from assumptions built into the simulations. We show that Monte Carlo simulations cannot produce knowledge other than by inference, and that they resemble other computer simulations in the manner in which they derive their conclusions. Simple examples of Monte Carlo simulations are analysed to identify the underlying inferences.

Faith as a Mustard Seed

Abstract: This investigation of the concept of faith is divided into two parts. Part One evaluates a topical philosophical interpretation of faith as irreducibly disjunctive, collecting the best fragmented ideas as to what constitutes faith in a recent family resemblance exposition as an objective for an adequate essentialist analysis of the concept of faith to achieve. Part Two offers a more extended essentialist analysis of the concept of faith as unconditional patience in the eventuality of a positive future state, and a detailed reduction of six supposedly disparate family resemblance senses of faith to this single definition. Criteria for a satisfactory analysis of faithfulness are considered and defended. In contrast with what has become a standard doxastic-epistemic interpretation of faith as persistent unjustified or even unjustifiable belief, a concept of faith is advanced that appears to satisfy the necessary and sufficient criteria identified. Systematic comparison with a variety of usages of the word “faith” suggests that the analysis agrees with many and arguably most applications of this sometimes loosely understood term. Implications of the analysis of the concept of faith are considered and defended against anticipated objections. Pascal’s wager is critically examined in relation to matters of religious faith, along with positivist meaningfulness requirements that seem to conflict especially with epistemically ungrounded belief, the power of faith, and the metaphorical size of mustard seeds. The inquiry concludes with a synthesis of five aspects of six supposedly distinct senses of faith under the single essentialist reductive umbrella of unconditional patience in the eventuality of a positive future state.

Intuitionistic common knowledge or belief

Starting off from the usual language of modal logic for multi-agent systems dealing with the agents’ knowledge/belief and common knowledge/belief we define so-called epistemic Kripke structures for intu- itionistic (common) knowledge/belief. Then we introduce corresponding deductive systems and show that they are sound and complete with respect to these semantics.