Related papers: Constrained Expressions and their Derivatives
Partial derivatives of regular expressions, introduced by Antimirov, define an elegant algorithm for generating equivalent non-deterministic finite automata (NFA) with a limited number of states. Here we focus on runtime verification (RV)…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
Recent years have witnessed a renewed interest in Boolean function in explaining binary classifiers in the field of explainable AI (XAI). The standard approach of Boolean function is propositional logic. We present a modal language of a…
A finite constraint language $\mathscr{R}$ is a finite set of relations over some finite domain $A$. We show that intractability of the constraint satisfaction problem $\operatorname{CSP}(\mathscr{R})$ can, in all known cases, be replaced…
In this paper, we investigate the use of selectional restriction -- the constraints a predicate imposes on its arguments -- in a language model for speech recognition. We use an un-tagged corpus, followed by a public domain tagger and a…
A temporal constraint language is a set of relations that are first-order definable over (Q;<). We show that several temporal constraint languages whose constraint satisfaction problem is maximally tractable are also maximally tractable for…
There has recently been an increasing interest in declarative data analysis, where analytic tasks are specified using a logical language, and their implementation and optimisation are delegated to a general-purpose query engine. Existing…
Path integral expressions for three canonical formalisms -- Ostrogradski's one, constrained one and generalized one -- of higher-derivative theories are given. For each fomalism we consider both nonsingular and singular cases. It is shown…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Length constraints restrict valid substitutions of…
Boyer and Moore have discussed a recursive function that puts conditional expressions into normal form [1]. It is difficult to prove that this function terminates on all inputs. Three termination proofs are compared: (1) using a measure…
We observe that the various formulations of the operational semantics of Constraint Handling Rules proposed over the years fall into a spectrum ranging from the analytical to the pragmatic. While existing analytical formulations facilitate…
Usually, probabilistic automata and probabilistic grammars have crisp symbols as inputs, which can be viewed as the formal models of computing with values. In this paper, we first introduce probabilistic automata and probabilistic grammars…
Nielsen transformations form the basis of a simple and widely used procedure for solving word equations. We make progress on the problem of determining when this procedure terminates in the presence of length constraints. To do this, we…
We explore language semantics for automata combining probabilistic and nondeterministic behavior. We first show that there are precisely two natural semantics for probabilistic automata with nondeterminism. For both choices, we show that…
Prolog is a well known declarative programming language based on propositional Horn formulas. It is useful in various areas, including artificial intelligence, automated theorem proving, mathematical logic and so on. An active research area…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
We present a metagrammatical formalism, {\em generic rules}, to give a default interpretation to grammar rules. Our formalism introduces a process of {\em dynamic binding} interfacing the level of pure grammatical knowledge representation…
Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…