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Many conditionals in natural language tend to be interpreted as biconditionals, where the antecedent is considered the single possible cause for the consequent to occur. However, there is no consensus about the factors that provoke or prevent a biconditional interpretation of the conditional. According to the theory that we want to test (von Fintel, 2001), a biconditional reading of a conditional, 'if p, q', is triggered if the conditional is understood as *exhaustive* list of sufficient conditions for the consequent. This is expected to be the case when the question-under-discussion puts the focus on the antecedent (e.g.under which conditions will q occur?). Since the conditional 'if p, q' mentions only one such condition (p), it is perfected and thus interpreted as biconditional. Contrary to that, the conditional, 'if p, q', is hypothesized not to be interpreted as biconditional, when the question-under-discussion puts the focus on the consequent, e.g. by a question-under-discussion about the consequences of the antecedent (e.g. what follows from p?).

One important controversy connected with the effectiveness of grammar teaching seems to have been resolved as there is ample empirical evidence testifying to the positive effect of form-focused instruction on second language acquisition (Nassaji & Fotos, 2004; Norris & Ortega, 2000; Spada, 1997, 2010). Nevertheless, there are still a number of problems open to debate and awaiting concrete solutions, such as how to establish connections between form and meaning and find the best way to teach grammar for implicit knowledge, which, in the opinion of most SLA researchers (Ellis, 2006a, p. 95) and according to numerous theoretical positions, is a key driver of linguistic competence. One of the options available to language educators is to employ focused communication tasks, which "are designed to elicit production of a specific target feature in the context of performing a communicative task" (Ellis, 2001, p. 21). The aim of the study reported in this article was to explore the effect of focused communication tasks on the instructed acquisition of English past counterfactual conditionals when compared with contextualized practice activities. The results of two types of intervention were measured employing a number of data collection instruments with a view to tapping both the explicit and implicit knowledge of the participants of the study. Both types of instructional treatment were equally effective in helping learners develop the explicit knowledge of past unreal conditionals, but when it comes to the implicit knowledge of the aforementioned structure, the group instructed by means of focused communication tasks outperformed the other experimental group and the control group, as evidenced by the results obtained from the individually elicited imitation test and the focused communication task performed in pairs.

There is a long-standing debate on whether humans are able to deal with probabilities in a way that reflects the normative standards of probability theory. In our second study, we focus on questions concerning probabilistic coherence in learning scenarios. The study extends on our previous explorative study (registered in the same project). It focuses on the differences between learning a conditional probability that is already (vacuously) believed to be true, versus cases where the conditional probability conflicts with the prior belief of the agent. In addition, it studies the effects of whether the learned conditional probability is low or high. From the normative perspective, these cases should be handled symmetrical but our previous study indicated notable differences between such cases.

According to Bayesianism, degrees of belief can be formalized in terms of probabilities, following the three Kolmogorov axioms. The conditional probability of a proposition C, given A is defined as Pr(C/A) = Pr(A&C)/Pr(A). A and C are said to be independent if and only if Pr(C)=Pr(C/A). Bayesianism comes with simple formalism for learning. If one learns evidence E, then the new degree of belief in a hypothesis H, Pr*(H), is given by the prior conditional probability P(H/E). This presupposes that the evidence has become certain, i.e., Pr*(E)=1. Jeffrey conditionalization, which is a sum of the update by E and -E, weighted by the respective new probability of E and -E, generalizes learning to cases where E is not certain. However, Jeffrey conditionalization cannot be used to learn a new conditional probability, such as the reliability or sensitivity of a test. The issue of how to learn conditional information is highly debated in philosophy, as exemplified in the large amount of literature on the so-called Judy Benjamin problem: Judy Benjamin has been dropped in an area with four quadrants (let us call them north-west, north-east, south-west, south-east). Her prior belief for being in any of them equals 1/4. She then receives the message that the probability that she is north given that she is west is 3/4. How can she update her beliefs in a way that will result in new probabilistically coherent credence? How can she do so and ensure that her new belief will be intuitively still close to her old one, i.e., epistemically conservative? While the problem of learning conditional information has received wide attention in (formal) epistemology, it has not been studied from a psychological perspective: How do lay people think about learning a new conditional probability? This will be the main question of our study. The study has two parts. The first one considers whether our participants answers are in line with probabilistic constraints. The second one focuses on whether their answers are conservative with respect to prior belief. We will do an exploratory study with two experiments to address these issues.

This paper discusses various controversies surrounding the meaning and use of such conditionals as A given B or If B then A including that such Boolean fractions 1) can non-trivially carry the standard conditional probability, 2) are truth functional but with three rather than two truth values, 3) are logically and probabilistically non-monotonic, 4) can be combined with operations that extend the standard Boolean operations, and 5) allow definitions that extend Boolean deduction but do not serve as deductions themselves thereby avoiding the so-called paradoxes identified by E. Adams. A new theory of deduction with uncertain conditionals is defined in terms of the new operations on conditionals by extending the familiar equations that define deduction between Boolean propositions. This leads to several plausible forms of deduction between conditionals. These different deductive relations on conditionals give rise to different sets of implications. Methods to determine the implications of one or more conditionals with respect to the various different deductive relations are described. Three examples of deduction with uncertain conditionals are extensively examined and solved. An example about an absent-minded coffee drinker contains two so-called subjunctive or counterfactual conditionals, which pose no additional difficulty. The issue of practical computation with conditionals is addressed and the use of information entropy to cut through complexity is discussed and illustrated. Lastly there is the question of how much confidence can be attached to a probability distribution having maximum entropy. In this regard the results of E. Jaynes concerning the concentration of distributions at maximum entropy are described along with two other theoretical approaches to this problem.