yusuke1997/dblp-id-title huggingface dataset:
Weakened Semantics and the Traditional Square of Opposition
Gentzen-Type Sequent Calculi for Extended Belnap-Dunn Logics with Classical Negation: A General Framework
Visual Clarity and Expressiveness in Logic Diagrams
On the Universality of Atomic and Molecular Logics via Protologics
Theological Discourse and Logic
A Universal Approach to Guarantee Data Privacy
Russell and His Sources for Non-Classical Logics
Frege's Ancestral and Its Circularities
Existence of Finite Total Equivalence Systems for Certain Closed Classes of 3-Valued Logic Functions
Translating Non-classical Logics into Classical Logic by Using Hidden Variables
Deduction as Reduction, from a Categorical Point of View
Rooted Hypersequent Calculus for Modal Logic S5
Dugundji's Theorem Revisited
Hypothetical Logic of Proofs
Understanding Money as a Communication Technology
Toward A Visual Proof System: Lewis Carroll's Method of Trees
A Buchholz Rule for Modal Fixed Point Logics
Developing Metalogic to Formalize Ontological Disputes of the Systems in Metaphysics by Introducing the Notion of Functionally Isomorphic Quantifiers
Non-Traditional Squares of Predication and Quantification
Singular Propositions, Negation and the Square of Opposition
Dagger Categories of Tame Relations
Epistemic Logics with Quantification Over Epistemic Operators: Decidability and Expressiveness
Unification in Pretabular Extensions of S4
A Note on a Description Logic of Concept and Role Typicality for Defeasible Reasoning Over Ontologies
Boethius of Dacia (1270s) and Radulphus Brito (1290s) on the Universal Sign 'Every'
Smurfing the Square of Opposition
To Peirce Hintikka's Thoughts
A Dialectic Contra-Classical Logic
Challenges in Formal Analysis of Resilience: Capturing the Tradeoff Between the Chance of Failure and the Cost of Success
The First Logic, Chance and Money Congress LoChaMo1, Las Vegas, Nevada, USA, November 2024 - Birth of a New Series of Logical Events
Bases for Structures and Theories I
Relative Contingency and Bimodality
Rejection: A Historico-Epistemological View
The Semiotics of Spider Diagrams
Islamic Contradictory Theology ... Is there any such Thing?
Graded Structures of Opposition in Fuzzy Natural Logic
Unified Deductive Systems: An Outline
Is Logic Necessary?
A Logical Analysis of the Anselm's Unum Argumentum (from Proslogion )
Toward a Clarity of the Extreme Value Theorem
On a Distinction of Two Facets of Meaning and its Role in Proof-theoretic Semantics
From the Logical Square to Blanché's Hexagon: Formalization, Applicability and the Idea of the Normative Structure of Thought
Universal Logic and Aristotelian Logic: Formality and Essence of Logic
Logic Diagrams, Sacred Geometry and Neural Networks
Theory of Semi-Instantiation in Abstract Argumentation
Modal Extensions of Sub-classical Logics for Recovering Classical Logic
Multimodal Incompleteness Under Weak Negations
The Sphere Model of Consciousness: From Geometrical to Neuro-Psycho-Educational Perspectives
Platonic Contrariety ( enantia ): Ancestor of the Aristotelian Notion of Contradiction ( antiphasis )?
Ockham's Calculus of Strict Implication
Paraconsistent Orbits of Logics
A Square of Oppositions in Intuitionistic Logic with Strong Negation
Brain and Its Universal Logical Model of Multi-Agent Biological Systems
Innovation and Application of Logic: An Interview with Jaakko Hintikka
Two Early Arabic Applications of Model-Theoretic Consequence
Leibniz's Logic and the "Cube of Opposition"
Non-monotonic Logic and the Compatibility of Science and Religion
Super Models
Operator Counterparts of Types of Reasoning
Revising the Elenchus via Belief Revision
Natural Deduction for Fitting's Four-Valued Generalizations of Kleene's Logics
Leibniz's Ontological Proof of the Existence of God and the Problem of »Impossible Objects«
Computer-Assisted Analysis of the Anderson-Hájek Ontological Controversy
On the 3D Visualisation of Logical Relations
Interconnection of the Lattices of Extensions of Four Logics
Quantifying Statements (Why 'Every Thing' is Not 'Everything', Among Other 'Thing's)
Implicational Partial Galois Logics: Relational Semantics
Weakening and Extending ℤ
Intensionality of Consequence and Identity of Proofs in Prawitz's Theory of Grounds
The Pursuit of an Implication for the Logics L3A and L3B
What is a Logic Translation?
On Consequence and Rejection as Operators
On the Origin of Logical Determinism in Babylonia
From Blanché's Hexagonal Organization of Concepts to Formal Concept Analysis and Possibility Theory
The Power of the Hexagon
Subalternation and existence presuppositions in an unconventionally formalized canonical square of opposition
Logic and Natural Selection
Forcing with Invariant Measures
On the Origin of Indian Logic from the Viewpoint of the Pāli Canon
A Note on Two's Company: "The Humbug of Many Logical Values"
A Universal Algebraic Set Theory Built on Mereology with Applications
Logical Extensions of Aristotle's Square
Kant's Antinomies of Pure Reason and the 'Hexagon of Predicate Negation'
An Intuitionist Reasoning Upon Formal Intuitionist Logic: Logical Analysis of Kolmogorov's 1932 Paper
Arbitrary Announcements in Social Networks: A Finitary Proof System
A Reinterpretation of the Semilattice Semantics with Applications
Direct Proofs of Lindenbaum Conditionals
Topological Representation of Intuitionistic and Distributive Abstract Logics
On Rereading van Heijenoort's Selected Essays
Essential Structure of Proofs as a Measure of Complexity
Can Formal Logic Make Pure Chance Intelligible? Ladrière on the Eschatological Horizon of Reason
A Unified Semantics for a Family of Modal Logics with Propositional Constants
Modelling Inference in Argumentation through Labelled Deduction: Formalization and Logical Properties
A Molecular Logic of Chords and Their Internal Harmony
Editor's Introduction to Jean van Heijenoort, Historical Development of Modern Logic
"Logical Lantern": Analogue of the Square of Opposition for Propositions in V.I. Markin's Universal Language for Traditional Positive Syllogistic Theories
A Short Note on Essentially Σ 1 Sentences
A Pragmatic Dissolution of Curry's Paradox
An Intensional Formalization of Generic Statements
Beppo Levi's Analysis of the Paradoxes
Intuitive Equilibriums in Games Like Traveler's Dilemma
Tableaux for Logics of Content Relationship and Set-Assignment Semantics
Birkhoff Completeness in Institutions
A Routley-Meyer Semantics for Gödel 3-Valued Logic and Its Paraconsistent Counterpart
Money, Time, and Information: Inspirations from Gödel, Tarski, and Chaitin
AI and the Visualization of Paradise: Cultural Paradigms, Aesthetic Evolution, and Cognitive Exploration
Universal Logic: Evolution of a Project
A Shared Framework for Consequence Operations and Abstract Model Theory
Cut-Free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics
Abstract Logical Constants
The Vatican Square
Things That are Right with the Traditional Square of Opposition
Generalized Definitional Reflection and the Inversion Principle
Encoding Complete Metric Structures by Classical Structures
Jean van Heijenoort's Contributions to Proof Theory and Its History
How to Take Advantage of the Blur Between the Finite and the Infinite
On a Generalization of Equilogical Spaces
Defining without Essences: Ibn Taymiyya's Critique of Aristotelian Logic
von Wright and Hintikka on Modal Logic 1951-1962
On the Mathematical Modeling in Logic: An Analysis of the Structural Part of Object Determination Logic Through the Formal Concept Analysis
On Transferring Model Theoretic Theorems of \({\mathcal{L}_{{\infty}, \omega}}\) in the Category of Sets to a Fixed Grothendieck Topos
Reflexivity of ømega-Consistency in a General Setting
Two Squares of Opposition in Two Arabic Treatises: al-Suhrawardī and al-Sanūsī
A Formalism to Specify Unambiguous Instructions Inspired by Mīmāṁsā in Computational Settings
Approaching the Alethic Modal Hexagon of Opposition
Existential Import, Aristotelian Logic, and its Generalizations
Frege's Ontological Diagram Completed
Swyneshed, Aristotle and the Rule of Contradictory Pairs
Which Mathematical Logic is the Logic of Mathematics?
Labelled Tableau Systems for Some Subintuitionistic Logics
Logical Rules as Fractions and Logics as Sketches
There is No Paradox of Logical Validity
Logical Consequence in Avicenna's Theory
The Institution-Theoretic Scope of Logic Theorems
The Classical Aristotelian Hexagon Versus the Modern Duality Hexagon
Disentangling Contradiction from Contrariety via Incompatibility
Venn i o1 : A Diagram System for Universe Without Boundary
Hintikka, Free Logician
The Oppositions of Categorical Propositions in Avicenna's Frame
Correction: Dynamic Oppositional Symmetries for Color, Jungian and Kantian Categories
A Characterisation of Some \(\mathbf {Z}\) -Like Logics
Monotonic and Non-monotonic Embeddings of Anselm's Proof
The Gambler's Fallacy and Its Impact on Business
Extracting BB′IW Inhabitants of Simple Types From Proofs in the Sequent Calculus ${LT_\to^{t}}$ for Implicational Ticket Entailment
Curry's Formalism as Structuralism
Symmetric Generalized Galois Logics
Towards a More General Concept of Inference
Preface: Is Logic Universal?
A Note on Fixed Points in Łukasiewicz Logic
A Note on Logicality of Generalized Quantifiers
Logic as Calculus Versus Logic as Language, Language as Calculus Versus Language as Universal Medium, and Syntax Versus Semantics
Analytics vs. Elements
An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras
Metalanguage and Revelation: Rethinking Theology's Language and Relevance
Compositional Meaning in Logic
Minimally Generated Abstract Logics
On TAE Machines and Their Computational Power
What do Freyd's Toposes Classify?
On the Road to Paradise: Some Logical Steps
A Methodological Shift in Favor of (Some) Paraconsistency in the Sciences
Modern Versus Classical Structures of Opposition: A Discussion
On the Logical Geometry of Geometric Angles
The Square of Opposition and the Four Fundamental Choices
Aristotle's Cubes and Consequential Implication
Universal Properties of Łukasiewicz Consequence
On Nonmonotonic Consequence Relations
Gödel's Second Theorem and the Provability of God's Existence
Elements of Categorical Logic: Fifty Years Later
The Talmudic Logic Project, Ongoing Since 2008
What is Money?
From Single Agent to Multi-Agent via Hypersequents
Iterated Mixed Strategies and Pascal's Wager
Jean van Heijenoort's Conception of Modern Logic, in Historical Perspective
Some Multi-Conclusion Modal Paralogics
The Decision Problem for Effective Procedures
General Logic-Systems and Finite Consequence Operators
Some Theorems of Birkhoff in Tonoid Matrices
Venn Diagram with Names of Individuals and Their Absence: A Non-classical Diagram Logic
Classical Negation Strikes Back: Why Priest's Attack on Classical Negation Can't Succeed
First-order Logics of Evidence and Truth with Constant and Variable Domains
An Extended Paradefinite Logic Combining Conflation, Paraconsistent Negation, Classical Negation, and Classical Implication: How to Construct Nice Gentzen-type Sequent Calculi
Splitting Property for Epistemic Equilibrium Logics
Constrained Pseudo-Propositional Logic
On the Shores of Dawn: The Logica in via Scoti and Its Logical Significance in Peru
On Refutation Rules
Structuring Co-constructive Logic for Proofs and Refutations
Logic and Religion
Finite Tree-Countermodels via Refutation Systems in Extensions of Positive Logic with Strong Negation
Why Make Things Simple When You Can Make Them Complicated? An Appreciation of Lewis Carroll's Symbolic Logic
Varieties of Rigidity
Morphisms Between Aristotelian Diagrams
Dung's Argumentation is Essentially Equivalent to Classical Propositional Logic with the Peirce-Quine Dagger
Kneale's Natural Deductions as a Notational Variant of Beth's Tableaus
Generalization and Composition of Modal Squares of Oppositions
Completeness: From Husserl to Carnap
Distributive-Lattice Semantics of Sequent Calculi with Structural Rules
Information Algebras and Consequence Operators
Logic as a Science and Logic as a Theory: Remarks on Frege, Russell and the Logocentric Predicament
Constrained Consequence
Composition-Nominative Logics as Institutions
From Fibring to Cryptofibring. A Solution to the Collapsing Problem
On Pairs of Dual Consequence Operations
Deontological Square, Hexagon, and Decagon: A Deontic Framework for Supererogation
From the Ontology of Money to Monetary Theory: Remarks on Inflation and Interest Rates
Preface to the Rejection Special Issue
Syllogisms and 5-Square of Opposition with Intermediate Quantifiers in Fuzzy Natural Logic
Adolf Lindenbaum: Notes on his Life, with Bibliography and Selected References
"Setting" n -Opposition
A Refutation Theory
Measuring Inconsistency in Generalized Propositional Logic
Expressivist Perspective on Logicality
Is the Principle of Contradiction a Consequence of \(x^{2}=x\) ?
Ultravaluations and their Applications in sfCPL
Perspectives on the Logical Study of Language
Axiomatisations of the Genuine Three-Valued Paraconsistent Logics $\mathbf {L3A_G}$ and $\mathbf {L3B_G}$
Correction to: Some Restricted Lindenbaum Theorems Equivalent to the Axiom of Choice
Liberating Paraconsistency from Contradiction
Hintikka Memorial Issue: Introduction and Remarks on Jaakko Hintikka's Logical Philosophy
Farewell to Suppression-Freedom
Human Rationality Challenges Universal Logic
Probabilization of Logics: Completeness and Decidability
The World Logic Prize - Third Edition of the World Logic Prizes Contest, 8 rmth UNILOG, Cusco, Peru, December 2025
Many-Place Sequent Calculi for Finitely-Valued Logics
Logic, Spatial Algorithms and Visual Reasoning
Calculi for Many-Valued Logics
The Role of the Common in Cognitive Prosperity: Our Command of the Unspeakable and Unwriteable
New Dimensions on Translations Between Logics
Rule-Elimination Theorems
Observation of Autonomous Behavioral Selection in Physarum Plasmodium
Mathematical Perspectives on Liar Paradoxes
Metalogical Decorations of Logical Diagrams
Logic Prizes et Cætera
A Hybrid Multi-Modal Logic for Context-Dependent Preferences
The Future of Logic: Foundation-Independence
Omnipresence, Multipresence and Ubiquity: Kinds of Generality in and Around Mathematics and Logics
Preface: Scope of Logic Theorems In Memoriam Adolf Lindenbaum
Negative Predication and Distinctness
A General Lindström Theorem for Some Normal Modal Logics
A New Modal Lindström Theorem
Structural Rules for Multi-valued Logics
The Method of Scientific Discovery in Peirce's Philosophy: Deduction, Induction, and Abduction
Visualizations of the Square of Opposition
Complementary Proof Nets for Classical Logic
Universal Principle of Consistency
Violence Hexagon
A Modern Rigorous Approach to Stratification in NF/NFU
The Meanings of 'Logic' in the Thirteenth Century
Historical Development of Modern Logic
On Rearrangement Inequalities for Triangular Norms and Co-norms in Multi-valued Logic
Philosophical Reflections: Chance, Determinism and Indeterminism
Bases for Structures and Theories II
The Klein Group, Squares of Opposition and the Explanation of Fallacies in Reasoning
The Geometry of Standard Deontic Logic
Recovering a Logic from Its Fragments by Meta-Fibring
A Global Glance on Categories in Logic
On Induction Principles for Partial Orders
Self-Extensional Three-Valued Paraconsistent Logics
Natural Deduction for Post's Logics and their Duals
What is Identical?
N.A. Vasil'ev's Logical Ideas and the Categorical Semantics of Many-Valued Logic
Varieties of Cubes of Opposition
A Reduction Theorem for the Kripke-Joyal Semantics: Forcing Over an Arbitrary Category can Always be Replaced by Forcing Over a Complete Heyting Algebra
Beyond Logical Pluralism and Logical Monism
Logics in Fungal Mycelium Networks
Jean van Heijenoort: Kaleidoscope
Abelian Logic and the Logics of Pointed Lattice-Ordered Varieties
Sound Reasoning (Literally): Prospects and Challenges of Current Acoustic Logics
Contrary-to-Duty Reasoning: A Categorical Approach
Things May Not Be Simple: On Wittgenstein's Internal Relations
A Categorical Interpretation of the Intuitionistic, Typed, First Order Logic with Hilbert's \({\varepsilon}\) -Terms
Inference Rules in Nelson's Logics, Admissibility and Weak Admissibility
On the Meaning of Connectives (Apropos of a Non-Necessitarianist Challenge)
The 2nd World Logic Prizes Contest, 7th UNILOG, Crete 2022
k-Provability in $\hbox {PA}$
Cubes and Hypercubes of Opposition, with Ethical Ruminations on Inviolability
The Logic of God: A Pluralistic Representational Theory of Concepts
A Strong and Rich 4-Valued Modal Logic Without Łukasiewicz-Type Paradoxes
Logical Squares for Classical Logic Sentences
Harmony in Multiple-Conclusion Natural-Deduction
Quantified Temporal Alethic Boulesic Doxastic Logic
On Non-Deterministic Quantification
Axiomatization of Some Basic and Modal Boolean Connexive Logics
Sequent Systems for Negative Modalities
On the Contingency of Logic in Possible World Semantics
John Buridan on the Bearer of Logical Relations
Positive Amalgamation
A Probabilistic Logic Between LPP 1 and LPP 2
The Normal and Self-extensional Extension of Dunn-Belnap Logic
Bimodal Logic with Contingency and Accident: Bisimulation and Axiomatizations
Ploucquet's "Refutation" of the Traditional Square of Opposition
1st World Logic Day: 14 January 2019
Tree-Like Proof Systems for Finitely-Many Valued Non-deterministic Consequence Relations
Applications of Squares of Oppositions and Their Generalizations in Philosophical Analysis
Probability Logics for Reasoning About Quantum Observations
The Buddhist Sengzhao's Roots in Daoism: Ex Contradictione Nihil
Guest Editor's Introduction: JvH100
Aristotle's Non-Logical Works and the Square of Oppositions in Semiotics
Duality Results for (Co)Residuated Lattices
On the Mosaic Method for Many-Dimensional Modal Logics: A Case Study Combining Tense and Modal Operators
Should We Embrace Impossible Worlds Due to the Flaws of Normal Modal Logic?
From Logic in Islam to Islamic Logic
Mathematics and Theology in the Thought of Nicholas of Cusa
Structuralist Logic: Implications, Inferences, and Consequences
Negation and Paraconsistent Logics
Logic and Colour
Canonical Syllogistic Moods in Traditional Aristotelian Logic
Scholarly Publications of Jean van Heijenoort Compiled by lrving H. Anellis
When the World is Not Enough: Medieval Ways to Deal with the Lack of Referents
The Place of Logic in Reasoning
On Preserving
Structuring the Universe of Universal Logic
Aristotle's Prototype Rule-Based Underlying Logic
Thomas Manlevelt: God in Logic
Referential Opacity and Epistemic Logic
Carnap, Goguen, and the Hyperontologies: Logical Pluralism and Heterogeneous Structuring in Ontology Design
Diagonalization in Double Frames
First-Order Logic and First-Order Functions
A Universal Logic Approach to Adaptive Logics
Beyond Rasiowan Systems: Unital Deductive Systems
From Analogical Proportion to Logical Proportions
The Square of Opposition and the Paradoxes
Why the Hexagon of Opposition is Really a Triangle: Logical Structures as Geometric Shapes
Abstract Categorical Logic
Dualities for Płonka Sums
On the Transitivity of Logical Consequence without Assuming Monotonicity
Dynamic Oppositional Symmetries for Color, Jungian and Kantian Categories
Paradox, Closure and Indirect Speech Reports
Forcing, Downward Löwenheim-Skolem and Omitting Types Theorems, Institutionally
Widersinn in Husserl's Pure Logic
Erratum to: Universal Logic and Aristotelian Logic: Formality and Essence of Logic
Generalized Correspondence Analysis for Three-Valued Logics
Characteristic Inference Rules
The Dynamics of Imperfect Reasoning: Change, Paraconsistency and Knowledge
Numerical Existence Property and Categories with an Internal Copy
The Cretan Square
Perfect IFG-Formulas
On a New Idiom in the Study of Entailment
In Defense of Logical Universalism: Taking Issue with Jean van Heijenoort
A Hexagonal Framework of the Field F 4 and the Associated Borromean Logic
The Logic with Truth and Falsehood Operators from a Point of View of Universal Logic
Mathematical Representation of Peterson's Rules for Fuzzy Peterson's Syllogisms
New Logics for Quantum Non-individuals?
Another Look at Modality and Connexivity
Abstract Logics, Logic Maps, and Logic Homomorphisms
Probabilistic Argumentation: An Equational Approach
From Varanasi to Sinaia
Correspondence Problems for Classes of Postlinear Orders
Pecularities of Some Three- and Four-Valued Second Order Logics
Canonical Extensions and Kripke-Galois Semantics for Non-distributive Logics
The Universalism of Logic in Stephen Langton's Analysis of the Blessing Given to Jacob
Stoic Sign-Inference and Their Lore of Fate
Why the Logical Hexagon?
Natural Deduction for Quantum Logic
Functorial Duality for Ortholattices and De Morgan Lattices
Positive Jonsson Theories
Equilibrium States in Numerical Argumentation Networks
Humanistic Demands and the Role of Chance in Business: A Plea for Mercy
The Universal Theory of First Order Algebras and Various Reducts
Is 'No' a Force-Indicator? Yes, Sooner or Later!
Counterpossibles and Normal Defaults in the Filioque Controversy
Meta-Arguments in Heterogeneous Logics and How to Evaluate Them
The Grammar of Platonism
A Logical Consequence Informed by Probability
A Galois Connection
Composition of Deductions within the Propositions-As-Types Paradigm
Modal Definability: Two Commuting Equivalence Relations
Inconsistency-Adaptive Dialogical Logic
Logic of Determination of Objects (LDO): How to Articulate "Extension" with "Intension" and "Objects" with "Concepts"
Intension and Dynamics: A Deductive Defense of Analogy
The Internal Logic and Finite Colimits
Measuring Inconsistency in Generalized Propositional Logic Extended with Nonunary Operators
Coproduct and Amalgamation of Deductive Systems by Means of Ordered Algebras
On the Paraconsistency of Argumentation Logic
Strong Normalizability of Typed Lambda-Calculi for Substructural Logics
Games and Lindström Theorems
An Idea Calculus For Natural and Artificial Intelligence
Thinking Negation in Early Hinduism and Classical Indian Philosophy
A Study of the Metatheory of Assertoric Syllogistic
Hintikka on the "Kant-Frege View": A Critical Assessment
Quotient Completion for the Foundation of Constructive Mathematics
On the Modal Logic of Jeffrey Conditionalization
On Combined Connectives
Crazy Dice, Chance, and Counting Causes
An Unexpected Boolean Connective
Jean van Heijenoort and the Gödel Editorial Project
Karma Theory, Determinism, Fatalism and Freedom of Will
Some Restricted Lindenbaum Theorems Equivalent to the Axiom of Choice
Quantified Multimodal Logics in Simple Type Theory
Hintikka and the Functions of Logic
Logic and the Social World
Some General Results About Proof Normalization
Lindenbaum-Type Logical Structures
Correspondence Analysis for Some Fragments of Classical Propositional Logic
Non-Classical Stems from Classical: N. A. Vasiliev's Approach to Logic and his Reassessment of the Square of Opposition
Consequence, Signification and Insolubles in Fourteenth-Century Logic
Modal Multilattice Logic
On the mathematics behind the entropy diversification measure in strategic management
Multi-objective unbalanced assignment problem with restriction of jobs to agents via NSGA-II
Analysis of non-pre-emptive priority retrial queueing system with two-way communication, Bernoulli vacation, collisions, working breakdown, immediate feedback and reneging
Performance analysis of a batch arrival retrial queue with Bernoulli feedback
Aspiration level-based non-dominated sorting genetic algorithm-II and III for multi-objective shortest path problem in a trapezoidal environment
Fuzzy transportation problem with hyperbolic function
Minimising vehicle distribution duration considering service priority
On optimality conditions for interval optimisation problems using generalised Hukuhara difference and constrained interval arithmetic
Water distribution networks leak detection using graph theory and optimised LSTM
A new agile fuzzy multi-objective model for selecting/eliminating supplier
Hermite Hadamard and Fejer type integral inequalities for harmonic convex (concave) fuzzy mappings
Measurable order and simulation
Optimal ordering policy for deteriorating items under down-stream trade credit dependent quadratic demand with full up-stream trade credit and partial down-stream trade credit