Whereas acausal Bayesian networks represent probabilistic independence, causal Bayesian networks represent causal relationships. In this paper, we examine Bayesian methods for learning both types of networks. Bayesian methods for learning acausal networks are fairly well developed. These methods often employ assumptions to facilitate the construction of priors, including the assumptions of parameter independence, parameter modularity, and likelihood equivalence. We show that although these assumptions also can be appropriate for learning causal networks, we need additional assumptions in order to learn causal networks. We introduce two sufficient assumptions, called mechanism independence and component independence. We show that these new assumptions, when combined with parameter independence, parameter modularity, and likelihood equivalence, allow us to apply methods for learning acausal networks to learn causal networks. 1

Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, and determination of liability. We present a formalism that uses probabilistic causal networks to evaluate one's belief that the counterfactual consequent, C, would have been true if the antecedent, A, were true. The antecedent of the query is interpreted as an external action that forces the proposition A to be true, which is consistent with Lewis' Miraculous Analysis. This formalism offers a concrete embodiment of the "closest world" approach which (1) properly reflects common understanding of causal influences, (2) deals with the uncertainties inherent in the world, and (3) is amenable to machine representation. Introduction A counterfactual sentence has the form If A were true, then C would have been true where A, the counterfactual antecedent, specifies an event that is contrary to one's real-world observations, and C, the counterfactual consequen...

This paper provides an update semantics for counterfactual conditionals. It does so by giving a dynamic twist to the ‘Premise Semantics ’ for counterfactuals developed in Veltman (1976) and Kratzer (1981). It also offers an alternative solution to the problems with naive Premise Semantics discussed by Angelika Kratzer in ‘Lumps of Thought ’ (Kratzer, 1989). Such an alternative is called for given the triviality results presented in Kanazawa et al. (2005, this issue). 1

Introduction. Our present concern originates with two uncontroversial observations about causation: the causal relation is asymmetric, so that if A is a cause of B then B is not a cause of A; and effects never (or almost never) occur before their causes. Uncontroversial as they may be, these features of causation are far from unproblematic. A philosophical theory of causation thus has these two non-trivial tasks, among others: to explicate the difference between cause and effect---to reveal the true content of the "arrow" of causation, so to speak---and to explain why the arrow of causation is so well aligned with the arrow of time. Note that the latter task permits two readings, depending on whether the temporal reference is read rigidly. On the stronger rigid or de re reading, the question is why the causal arrow points in this particular temporal direction, thought of as fixed independently of our disposition to treat the direction in question as that

In this paper I explore the possibilities for developing a formal language containing both tense and conditional operators and a model theory for such a language. 1 The criteria for success will be that we may provide formal counterparts for a wide variety of English conditionals and that the truth conditions for these formal counterparts will be appropriate for the English conditionals which they represent. Temporal relations play an essential role in determining the truth values of many and perhaps most conditional assertions. This fact is recognized and explored by many logicians including David Lewis (1979) and John Pollock (1981), yet the attention which investigators of the logic of conditionals have given to temporal relations has not in general included an explicit consideration of the interaction of tense and conditional constructions. Two exceptions are Thomason and Gupta (1980) and van Fraassen (1980) who do develop an account of the logical and semantical properties of c...

of this material. This paper was stimulated by thinking through the Gibbard phenomenon with students from my class on conditionals at the University of Leeds in 2006. Thanks to all involved. 1 I outline and motivate a way of implementing a closest world theory of indicatives, appealing to Stalnaker’s framework of open conversational possibilities. Stalnakerian conversational dynamics helps us resolve two outstanding puzzles for a such a theory of indicative conditionals. The first puzzle—concerning so-called ‘reverse Sobel sequences’—can be resolved by conversation dynamics in a theory-neutral way: the explanation works as much for Lewisian counterfactuals as for the account of indicatives developed here. Resolving the second puzzle, by contrast, relies on the interplay between the particular theory of indicative conditionals developed here and Stalnakerian dynamics. The upshot is an attractive resolution of the so-called “Gibbard phenomenon ” for indicative conditionals. Stalnakerian conversational dynamics can help us resolve two outstanding puzzles for a “closest-world ” modal theory of indicative conditionals. I begin the paper by outlining and motivating a new way of implementing a closest world theory of indicatives, appealing to Stalnaker’s framework of open conversational possibilities. Stalnaker’s framework itself shows its utility in application to condi-tionals by allowing us to explain a puzzling feature of conditionals—concerning so-called ‘reverse Sobel sequences’—in a theory-neutral way. The explanation has application to any “closest worlds ” account of indicative or counterfactual conditionals, as well as to other truth-conditional accounts of conditionals. My favoured closest world theory of indicative conditionals, when combined with Stalnakerian dynamics, gives an attractive resolution of the so-called “Gibbard phenomenon ” for indicative conditionals. 1

John Hawthorne in a recent paper takes issue with Lewisian accounts of counterfactuals, when relevant laws of nature are chancy. I respond to his arguments on behalf of the Lewisian, and conclude that while some can be rebutted, the case against the original Lewisian account is strong. I develop a neo-Lewisian account of what makes for closeness of worlds. I argue that my revised version avoids Hawthorne’s challenges. I argue that this is closer to the spirit of Lewis’s first (non-chancy) proposal than is Lewis’s own suggested modification. 1 Counterfactuals and Chance The antecedents of some counterfactual statements render their consequent hugely probable, but not certainly true. That is, it is not impossible that a combination of unlikely coincidences could lead to a situation in which the antecedent is true and the consequent false. For example: (A) If I were to toss this fair coin 10,000,000 times, it would not come up heads every time.

This paper is the most complete presentation of my views on deterministic causation. It develops the deterministic theory in perfect parallel to my theory of probabilistic causation and thus unites the two aspects. It also argues that the theory presented is superior to all regularity and all counterfactual theories of causation.

Counterfactuals in quantum mechanics appear in discussions of a) nonlocality, b) pre- and post-selected systems, and c) interaction-free measurements. Only the first two issues are related to counterfactuals as they are considered in the general philosophical literature: If it were that A, then it would be that B. The truth value of a counterfactual is decided by the analysis of similarities between the actual and possible counterfactual worlds [1]. The difference between a counterfactual (or counterfactual conditional) and a simple conditional: If A, then B, is that in the actual world A is not true and we need some “miracle ” in the counterfactual world to make it true. In the analysis of counterfactuals out of the scope of physics, this miracle is crucial for deciding whether B is true. In physics, however, miracles are not involved. Typically: A: A measurement M is performed B: The outcome of M has property P.