Related papers: Computing Theory Prime Implicates in Modal Logic

We introduce a novel logical notion--partial entailment--to propositional logic. In contrast with classical entailment, that a formula P partially entails another formula Q with respect to a background formula set \Gamma intuitively means…

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…

In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…

With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic…

Many multiagent applications require an agent to learn quickly how to interact with previously unknown other agents. To address this problem, researchers have studied learning algorithms which compute posterior beliefs over a hypothesised…

This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…

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 establish a generic upper bound ExpTime for reasoning with global assumptions (also known as TBoxes) in coalgebraic modal logics. Unlike earlier results of this kind, our bound does not require a tractable set of tableau rules for the…

We extend the logical categories framework to first order modal logic. In our modal categories, modal operators are applied directly to subobjects and interact with the background factorization system. We prove a Joyal-style representation…

Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…

Science consists on conceiving hypotheses, confronting them with empirical evidence, and keeping only hypotheses which have not yet been falsified. Under deductive reasoning they are conceived in view of a theory and confronted with…

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…

Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…

In this paper, an application of automated theorem proving techniques to computational semantics is considered. In order to compute the presuppositions of a natural language discourse, several inference tasks arise. Instead of treating…

This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with…

Data analytics often involves hypothetical reasoning: repeatedly modifying the data and observing the induced effect on the computation result of a data-centric application. Previous work has shown that fine-grained data provenance can help…

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…

While previous sentiment analysis research has concentrated on the interpretation of explicitly stated opinions and attitudes, this work initiates the computational study of a type of opinion implicature (i.e., opinion-oriented inference)…

An important open question in AI is what simple and natural principle enables a machine to reason logically for meaningful abstraction with grounded symbols. This paper explores a conceptually new approach to combining probabilistic…