Related papers: Interpreting connexive principles in coherence-bas…
We present a novel approach to constraint-based causal discovery, that takes the form of straightforward logical inference, applied to a list of simple, logical statements about causal relations that are derived directly from observed…
Abductive reasoning aims to find plausible explanations for an event. This style of reasoning is critical for commonsense tasks where there are often multiple plausible explanations. Existing approaches for abductive reasoning in natural…
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…
The Logic of Approximate Entailment (LAE) is a graded counterpart of classical propositional calculus, where conclusions that are only approximately correct can be drawn. This is achieved by equipping the underlying set of possible worlds…
In our previous work, we proposed the logic obtained from full non-associative Lambek calculus by adding a sort of linear-logical modality. We call this logic non-associative non-commutative intuitionistic linear logic ($\mathbf{NACILL}$,…
It is well-known that intuitionistic logics can be formalized by means of Brouwerian semilattices, i.e. relatively pseudocomplemented semilattices. Then the logical connective implication is considered to be the relative pseudocomplement…
Humans currently use arguments for explaining choices which are already made, or for evaluating potential choices. Each potential choice has usually pros and cons of various strengths. In spite of the usefulness of arguments in a decision…
We propose an inequality paradigm for probabilistic reasoning based on a logic of upper and lower bounds on conditional probabilities. We investigate a family of probabilistic logics, generalizing the work of Nilsson [14]. We develop a…
There are multiple proposed interpretations of probability theory: one such interpretation is true-false logic under uncertainty. Cox's Theorem is a representation theorem that states, under a certain set of axioms describing the meaning of…
A fundamental question in causal inference is whether it is possible to reliably infer manipulation effects from observational data. There are a variety of senses of asymptotic reliability in the statistical literature, among which the most…
It has been widely acknowledged that probabilistic independence and logical independence cannot be coherently reconciled. By bridging these two notions, this paper addresses three long-standing problems that have puzzled the field of…
The objective of this paper is to present general, mechanically verified, refinement rules for reasoning about recursive programs and while loops in the context of concurrency. Unlike many approaches to concurrency, we do not assume that…
This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories, it investigates whether intuitions about intrinsic time directedness that are often associated with…
When knowledge is obtained from a database, it is only possible to deduce confidence intervals for probability values. With confidence intervals replacing point values, the results in the set covering model include interval constraints for…
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…
A new computational method is presented to implement the system of deductive logic described by Aristotle in Prior Analytics. Each Aristotelian problem is interpreted as a parametric probability network in which the premises give…
We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the…
We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…
We introduce a formal logical language, called conditional probability logic (CPL), which extends first-order logic and which can express probabilities, conditional probabilities and which can compare conditional probabilities. Intuitively…
This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by W. Cooper and yields two logics of…