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The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…
Commonsense reasoning has long been considered as one of the holy grails of artificial intelligence. Most of the recent progress in the field has been achieved by novel machine learning algorithms for natural language processing. However,…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed…
Probabilistic coupling is a powerful tool for analyzing pairs of probabilistic processes. Roughly, coupling two processes requires finding an appropriate witness process that models both processes in the same probability space. Couplings…
Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…
We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
A notion of probabilistic lambda-calculus usually comes with a prescribed reduction strategy, typically call-by-name or call-by-value, as the calculus is non-confluent and these strategies yield different results. This is a break with one…
Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational…
A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a…
Subgraph Isomorphism uses a small graph as a pattern to identify within a larger graph a set of vertices that have matching edges. This paper addresses a logic program written in Prolog for a specific relatively complex graph pattern for…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise)…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
The complete reason behind a decision is a Boolean formula that characterizes why the decision was made. This recently introduced notion has a number of applications, which include generating explanations, detecting decision bias and…
Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…