12 research outputs found
Embedding Non-Ground Logic Programs into Autoepistemic Logic for Knowledge Base Combination
In the context of the Semantic Web, several approaches to the combination of
ontologies, given in terms of theories of classical first-order logic and rule
bases, have been proposed. They either cast rules into classical logic or limit
the interaction between rules and ontologies. Autoepistemic logic (AEL) is an
attractive formalism which allows to overcome these limitations, by serving as
a uniform host language to embed ontologies and nonmonotonic logic programs
into it. For the latter, so far only the propositional setting has been
considered. In this paper, we present three embeddings of normal and three
embeddings of disjunctive non-ground logic programs under the stable model
semantics into first-order AEL. While the embeddings all correspond with
respect to objective ground atoms, differences arise when considering
non-atomic formulas and combinations with first-order theories. We compare the
embeddings with respect to stable expansions and autoepistemic consequences,
considering the embeddings by themselves, as well as combinations with
classical theories. Our results reveal differences and correspondences of the
embeddings and provide useful guidance in the choice of a particular embedding
for knowledge combination.Comment: 52 pages, submitte
Implementing Default and Autoepistemic Logics via the Logic of GK
The logic of knowledge and justified assumptions, also known as logic of
grounded knowledge (GK), was proposed by Lin and Shoham as a general logic for
nonmonotonic reasoning. To date, it has been used to embed in it default logic
(propositional case), autoepistemic logic, Turner's logic of universal
causation, and general logic programming under stable model semantics. Besides
showing the generality of GK as a logic for nonmonotonic reasoning, these
embeddings shed light on the relationships among these other logics. In this
paper, for the first time, we show how the logic of GK can be embedded into
disjunctive logic programming in a polynomial but non-modular translation with
new variables. The result can then be used to compute the extension/expansion
semantics of default logic, autoepistemic logic and Turner's logic of universal
causation by disjunctive ASP solvers such as claspD(-2), DLV, GNT and cmodels.Comment: Proceedings of the 15th International Workshop on Non-Monotonic
Reasoning (NMR 2014
Semantics of logic programs with explicit negation
After a historical introduction, the bulk of the thesis concerns the study of a declarative semantics for logic programs. The main original contributions are: ² WFSX (Well–Founded Semantics with eXplicit negation), a new semantics for logic programs with explicit negation (i.e. extended logic programs), which compares favourably in its properties with other extant semantics. ² A generic characterization schema that facilitates comparisons among a diversity of semantics of extended logic programs, including WFSX. ² An autoepistemic and a default logic corresponding to WFSX, which solve existing problems of the classical approaches to autoepistemic and default logics, and clarify the meaning of explicit negation in logic programs. ² A framework for defining a spectrum of semantics of extended logic programs based on the abduction of negative hypotheses. This framework allows for the characterization of different levels of scepticism/credulity, consensuality, and argumentation. One of the semantics of abduction coincides with WFSX. ² O–semantics, a semantics that uniquely adds more CWA hypotheses to WFSX. The techniques used for doing so are applicable as well to the well–founded semantics of normal logic programs. ² By introducing explicit negation into logic programs contradiction may appear. I present two approaches for dealing with contradiction, and show their equivalence. One of the approaches consists in avoiding contradiction, and is based on restrictions in the adoption of abductive hypotheses. The other approach consists in removing contradiction, and is based in a transformation of contradictory programs into noncontradictory ones, guided by the reasons for contradiction
Multi-Agent Only Knowing
Levesque introduced a notion of ``only knowing'', with the goal of capturing
certain types of nonmonotonic reasoning. Levesque's logic dealt with only the
case of a single agent. Recently, both Halpern and Lakemeyer independently
attempted to extend Levesque's logic to the multi-agent case. Although there
are a number of similarities in their approaches, there are some significant
differences. In this paper, we reexamine the notion of only knowing, going back
to first principles. In the process, we simplify Levesque's completeness proof,
and point out some problems with the earlier definitions. This leads us to
reconsider what the properties of only knowing ought to be. We provide an axiom
system that captures our desiderata, and show that it has a semantics that
corresponds to it. The axiom system has an added feature of interest: it
includes a modal operator for satisfiability, and thus provides a complete
axiomatization for satisfiability in the logic K45.Comment: To appear, Journal of Logic and Computatio
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Using Extended Logic Programs to Formalize Commonsense Reasoning
In this dissertation, we investigate how commonsense reasoning can be formalized by using extended logic programs. In this investigation, we first use extended logic programs to formalize inheritance hierarchies with exceptions by adopting McCarthy's simple abnormality formalism to express uncertain knowledge. In our representation, not only credulous reasoning can be performed but also the ambiguity-blocking inheritance and the ambiguity-propagating inheritance in skeptical reasoning are simulated. In response to the anomalous extension problem, we explore and discover that the intuition underlying commonsense reasoning is a kind of forward reasoning. The unidirectional nature of this reasoning is applied by many reformulations of the Yale shooting problem to exclude the undesired conclusion. We then identify defeasible conclusions in our representation based on the syntax of extended logic programs. A similar idea is also applied to other formalizations of commonsense reasoning to achieve such a purpose
Current and Future Challenges in Knowledge Representation and Reasoning
Knowledge Representation and Reasoning is a central, longstanding, and active
area of Artificial Intelligence. Over the years it has evolved significantly;
more recently it has been challenged and complemented by research in areas such
as machine learning and reasoning under uncertainty. In July 2022 a Dagstuhl
Perspectives workshop was held on Knowledge Representation and Reasoning. The
goal of the workshop was to describe the state of the art in the field,
including its relation with other areas, its shortcomings and strengths,
together with recommendations for future progress. We developed this manifesto
based on the presentations, panels, working groups, and discussions that took
place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge
Representation: its origins, goals, milestones, and current foci; its relation
to other disciplines, especially to Artificial Intelligence; and on its
challenges, along with key priorities for the next decade
Epistemic extensions of answer set programming
but due to the non-monotonic nature of ASP; the weight can reflect the certainty that the rule itself is correct. ASP programs with incorrect rules may have erroneous conclusions; omitting a correct rule may also lead to errors. To derive the most certain conclusions from an uncertain ASP program; the weight can reflect the certainty with which we can conclude the head of a rule when its body is satisfied. This corresponds with how the weight is understood when defining semantics for PASP in terms of constraints on possibility distributions. On the other hand; we highlight how the weight attached to a rule in PASP can be interpreted in different ways. On the one hand; some decision problems are easier.
Thirdly; while the complexity of most reasoning tasks coincides with disjunction in ordinary ASP; called weak disjunction; that has not been previously considered in the ASP literature. When examining the complexity of weak disjunction we unearth that; we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction; since ASP is a special case of PASP in which all the rules are entirely certain; we show how semantics for PASP can be defined in terms of constraints on possibility distributions. These new semantics adhere to a different intuition for negation-as-failure than current work on PASP to avoid unintuitive conclusions in specific settings. In addition; where the first leader has the first say and may remove models that he or she finds unsatisfactory. Using this particular communication mechanism allows us to capture the entire polynomial hierarchy.
Secondly; where each program in the sequence may successively remove some of the remaining models. This mimics a sequence of leaders; we modify the communication mechanism to also allow us to focus on a sequence of communicating programs; it is shown that the addition of this easy form of communication allows us to move one step up in the polynomial hierarchy. Furthermore; i.e. they can communicate. For the least complex variant of ASP; simple programs; one ASP program can conceptually query another program as to whether it believes some literal to be true or not; which is a framework that allows us to study the formal properties of communication and the complexity of the resulting system in ASP. It is based on an extension of ASP in which we consider a network of ordinary ASP programs. These communicating programs are extended with a new kind of literal based on the notion of asking questions. As such; we introduce Communicating Answer Set Programming (CASP); namely Possibilistic Answer Set Programming (PASP); there are contexts in which the current semantics for PASP lead to unintuitive results.
In this thesis we address these issues in the followings ways. Firstly; ASP lacks the means to easily model and reason about uncertain information. While extensions of ASP have been proposed to deal with uncertainty; where each context encodes a different aspect of the real world. Extensions of ASP have been proposed to model such multi-context systems; but the exact effect of communication on the overall expressiveness remains unclear. In addition; it is not an ideal framework to model common-sense reasoning. For example; in ASP we cannot model multi-context systems; while ASP similarly allows us to revise knowledge; we conclude that the bird can fly. When new knowledge becomes available (e.g. the bird is a penguin) we may need to retract conclusions. However; in common-sense reasoning; Answer Set Programming (ASP) is a declarative programming language based on the stable model semantics and geared towards solving complex combinatorial problems. The strength of ASP stems from the use of a non-monotonic operator. This operator allows us to retract previously made conclusions as new information becomes available. Similarly; we may arrive at conclusions based on the absence of information. When an animal is for example a bird; and we do not know that this bird is a penguin; we thus need to consider all situations in which some; none; or all of the least certain rules are omitted. This corresponds to treating some rules as optional and reasoning about which conclusions remain valid regardless of the inclusion of these optional rules. Semantics for PASP are introduced based on this idea and it is shown that some interesting problems in Artificial Intelligence can be expressed in terms of optional rules.
For both CASP and the new semantics for PASP we show that most of the concepts that we introduced can be simulated using classical ASP. This provides us with implementations of these concepts and furthermore allows us to benefit from the performance of state-of-the-art ASP solvers