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Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…
We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
Fact verification on tabular evidence incentivises the use of symbolic reasoning models where a logical form is constructed (e.g. a LISP-style program), providing greater verifiability than fully neural approaches. However, these systems…
We introduce SMProbLog, a generalization of the probabilistic logic programming language ProbLog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly…
While there is a long tradition of reasoning about (non)termination in program analysis, specialized logics are typically needed to give different termination criteria. This includes partial correctness, where termination is not guaranteed,…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…
A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…
Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We give an optimal (EXPTIME), sound and complete tableau-based algorithm for deciding satisfiability for propositional dynamic logic with converse (CPDL) which does not require the use of analytic cut. Our main contribution is a sound…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
Higher-level cognition includes logical reasoning and the ability of question answering with common sense. The RatioLog project addresses the problem of rational reasoning in deep question answering by methods from automated deduction and…
A logic programming paradigm which expresses solutions to problems as stable models has recently been promoted as a declarative approach to solving various combinatorial and search problems, including planning problems. In this paradigm,…
Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…
Table reasoning, a task to answer questions by reasoning over data presented in tables, is an important topic due to the prevalence of knowledge stored in tabular formats. Recent solutions use Large Language Models (LLMs), exploiting the…
Despite recent advances in modern machine learning algorithms, the opaqueness of their underlying mechanisms continues to be an obstacle in adoption. To instill confidence and trust in artificial intelligence systems, Explainable Artificial…
This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give…