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The unification of logic and probability is a long-standing concern in AI, and more generally, in the philosophy of science. In essence, logic provides an easy way to specify properties that must hold in every possible world, and…
When dealing with process calculi and automata which express both nondeterministic and probabilistic behavior, it is customary to introduce the notion of scheduler to solve the nondeterminism. It has been observed that for certain…
The structure of a sentence can be represented as a network where vertices are words and edges indicate syntactic dependencies. Interestingly, crossing syntactic dependencies have been observed to be infrequent in human languages. This…
The paper demonstrates that strict adherence to probability theory does not preclude the use of concurrent, self-activated constraint-propagation mechanisms for managing uncertainty. Maintaining local records of sources-of-belief allows…
Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief…
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…
Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis earlier considered such a notion of relative likelihood in the…
Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
Many forecasts consist not of point predictions but concern the evolution of quantities. For example, a central bank might predict the interest rates during the next quarter, an epidemiologist might predict trajectories of infection rates,…
At the beginning of a dynamic game, players may have exogenous theories about how the opponents are going to play. Suppose that these theories are commonly known. Then, players will refine their first-order beliefs, and challenge their own…
Ratios of universal enumerable semimeasures corresponding to hypotheses are investigated as a solution for statistical composite hypotheses testing if an unbounded amount of computation time can be assumed. Influence testing for discrete…
This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
Strict frequentism defines probability as the limiting relative frequency in an infinite sequence. What if the limit does not exist? We present a broader theory, which is applicable also to random phenomena that exhibit diverging relative…
Human reasoning often involves working over limited information to arrive at probabilistic conclusions. In its simplest form, this involves making an inference that is not strictly entailed by a premise, but rather only likely given the…
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are…
It is often argued that bottom-up causation under a physicalist, reductionist worldview precludes free will in the libertarian sense. On the one hand, the paradigm of classical mechanics makes determinism inescapable, while on the other,…
In many situations people make sequences of similar, but unrelated decisions. Such decision sequences are prevalent in many important contexts including judicial judgments, loan approvals, college admissions, and athletic competitions. A…
The idea of fully accepting statements when the evidence has rendered them probable enough faces a number of difficulties. We leave the interpretation of probability largely open, but attempt to suggest a contextual approach to full belief.…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…