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The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
A proof tableau of Hoare logic is an annotated program with pre- and post-conditions, which corresponds to an inference tree of Hoare logic. In this paper, we show that a proof tableau for partial correctness can be transformed into an…
We propose an algebraic model of computation which formally relates symbolic listings, complexity of Boolean functions, and low depth arithmetic circuit complexity. In this model algorithms are arithmetic formula expressing symbolic…
Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary…
We introduce and address the problem of ad hoc table retrieval: answering a keyword query with a ranked list of tables. This task is not only interesting on its own account, but is also being used as a core component in many other…
Recent work demonstrated the existence of critical flaws in the current use of Shapley values in explainable AI (XAI), i.e. the so-called SHAP scores. These flaws are significant in that the scores provided to a human decision-maker can be…
We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may…
We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…
Combining knowledge and beliefs of autonomous peers in distributed settings, is a ma- jor challenge. In this paper we consider peers that combine ontologies and reason jointly with their coupled knowledge. Ontologies are within the SHIQ…
Bernays introduced a method for proving underivability results in propositional calculi by truth tables. In general, this motivates an investigations of how to find, given a propositional logic, a finite-valued logic which has as few…
Compositional models were introduce by Jirousek and Shenoy in the general framework of valuation-based systems. They based their theory on an axiomatic system of valuations involving not only the operations of combination and…
In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notion of evaluation. We investigate properties of such…
We discuss tableaux for the Implicational Propositional Calculus and show how they may be used to establish its completeness.
We introduce an extension of the propositional calculus to include abstracts of predicates and quantifiers, employing a single rule along with a novel comprehension schema and a principle of extensionality, which are substituted for the…
This paper describes how automated deduction methods for natural language processing can be applied more efficiently by encoding context in a more elaborate way. Our work is based on formal approaches to context, and we provide a tableau…
The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.
In this short note we relate some known properties of propositional calculus to purely algebraic considerations of a Boolean algebra. Classes of formulas of propositional calculus are considered as elements of a Boolean algebra. As such…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
This paper presents a tableau calculus for finding a model for a set-satisfiable finite set of formulas of an extended fuzzy logic BL, a fuzzy logic BL with additional Baaz connective and the involutive negation, if such a model exists. The…
There have been several recent suggestions for tableau systems for deciding satisfiability in the practically important branching time temporal logic known as CTL*. In this paper we present a streamlined and more traditional tableau…